Improved comprehensibility and reliability of explanations via restricted halfspace discretization

Abstract. A number of two-class classification methods first discretize each attribute of two given training sets and then construct a propositional DNF formula that evaluates to True for one of the two discretized training sets and to False for the other one. The formula is not just a classification tool but constitutes a useful explanation for the differences between the two underlying populations if it can be comprehended by humans and is reliable. This paper shows that comprehensibility as well as reliability of the formulas can sometimes be improved using a discretization scheme where linear combinations of a small number of attributes are discretized

HIV Cell-to-Cell Spread Results in Earlier Onset of Viral Gene Expression by Multiple Infections per Cell

Cell-to-cell spread of HIV, a directed mode of viral transmission, has been observed to be more rapid than cell-free infection. However, a mechanism for earlier onset of viral gene expression in cell-to-cell spread was previously uncharacterized. Here we used time-lapse microscopy combined with automated image analysis to quantify the timing of the onset of HIV gene expression in a fluorescent reporter cell line, as well as single cell staining for infection over time in primary cells. We compared cell-to-cell spread of HIV to cell-free infection, and limited both types of transmission to a two-hour window to minimize differences due to virus transit time to the cell. The mean time to detectable onset of viral gene expression in cell-to-cell spread was accelerated by 19% in the reporter cell line and by 35% in peripheral blood mononuclear cells relative to cell-free HIV infection. Neither factors secreted by infected cells, nor contact with infected cells in the absence of transmission, detectably changed onset. We recapitulated the earlier onset by infecting with multiple cell-free viruses per cell. Surprisingly, the acceleration in onset of viral gene expression was not explained by cooperativity between infecting virions. Instead, more rapid onset was consistent with a model where the fastest expressing virus out of the infecting virus pool sets the time for infection independently of the other co-infecting viruses

Internet of Things for Sustainable Mining

The sustainable mining Internet of Things deals with the applications of IoT technology to the coupled needs of sustainable recovery of metals and a healthy environment for a thriving planet. In this chapter, the IoT architecture and technology is presented to support development of a digital mining platform emphasizing the exploration of rock–fluid–environment interactions to develop extraction methods with maximum economic benefit, while maintaining and preserving both water quantity and quality, soil, and, ultimately, human health. New perspectives are provided for IoT applications in developing new mineral resources, improved management of tailings, monitoring and mitigating contamination from mining. Moreover, tools to assess the environmental and social impacts of mining including the demands on dwindling freshwater resources. The cutting-edge technologies that could be leveraged to develop the state-of-the-art sustainable mining IoT paradigm are also discussed

Data-driven discovery of Green’s functions with human-understandable deep learning

There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. We develop a novel data-driven approach for creating a human-machine partnership to accelerate scientific discovery. By collecting physical system responses, under carefully selected excitations, we train rational neural networks to learn Green's functions of hidden partial differential equation. These solutions reveal human-understandable properties and features, such as linear conservation laws, and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate this technique on several examples and capture a range of physics, including advection-diffusion, viscous shocks, and Stokes flow in a lid-driven cavity

Computing with functions in the ball

A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine precision by using a three-dimensional analogue of the double Fourier sphere method to form “Ballfun" objects. Operations such as function evaluation, differentiation, integration, fast rotation by an Euler angle, and a Helmholtz solver are designed. Our algorithms are particularly efficient for vector calculus operations, and we describe how to compute the poloidal-toroidal and Helmholtz--Hodge decompositions of a vector field defined on the ball

Learning Elliptic Partial Differential Equations with Randomized Linear Algebra

AbstractGiven input–output pairs of an elliptic partial differential equation (PDE) in three dimensions, we derive the first theoretically rigorous scheme for learning the associated Green’s function G. By exploiting the hierarchical low-rank structure of G, we show that one can construct an approximant to G that converges almost surely and achieves a relative error of $$\mathcal {O}(\varGamma _\epsilon ^{-1/2}\log ^3(1/\epsilon )\epsilon )$$ O ( Γ ϵ - 1 / 2 log 3 ( 1 / ϵ ) ϵ ) using at most $$\mathcal {O}(\epsilon ^{-6}\log ^4(1/\epsilon ))$$ O ( ϵ - 6 log 4 ( 1 / ϵ ) ) input–output training pairs with high probability, for any 0<\epsilon <1 0 &lt; ϵ &lt; 1 . The quantity 0<\varGamma _\epsilon \le 1 0 &lt; Γ ϵ ≤ 1 characterizes the quality of the training dataset. Along the way, we extend the randomized singular value decomposition algorithm for learning matrices to Hilbert–Schmidt operators and characterize the quality of covariance kernels for PDE learning.</jats:p

A GENERALIZATION OF THE RANDOMIZED SINGULAR VALUE DECOMPOSITION

The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank k approximation of a matrix A using matrix-vector products with standard Gaussian vectors. Here, we generalize the randomized SVD to multivariate Gaussian vectors, allowing one to incorporate prior knowledge of A into the algorithm. This enables us to explore the continuous analogue of the randomized SVD for Hilbert-Schmidt (HS) operators using operator-function products with functions drawn from a Gaussian process (GP). We then construct a new covariance kernel for GPs, based on weighted Jacobi polynomials, which allows us to rapidly sample the GP and control the smoothness of the randomly generated functions. Numerical examples on matrices and HS operators demonstrate the applicability of the algorithm

Rational neural networks

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks with exponentially smaller depth. The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU, as we demonstrate with numerical experiments

CONTROL OF BIFURCATION STRUCTURES USING SHAPE OPTIMIZATION

Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability or bring forward a bifurcation to enable rapid switching between states. We propose a numerical technique for controlling the bifurcation diagram of a nonlinear partial differential equation by varying the shape of the domain. Specifically, we are able to delay or advance a given branch point to a target parameter value. The algorithm consists of solving a shape optimization problem constrained by an augmented system of equations, the Moore-Spence system, that characterize the location of the branch points. Numerical experiments on the Allen-Cahn, Navier-Stokes, and hyperelasticity equations demonstrate the effectiveness of this technique in a wide range of settings