### Improving Model Robustness Using Causal Knowledge. (arXiv:1911.12441v1 [cs.LG])

For decades, researchers in fields, such as the natural and social sciences, have been verifying causal relationships and investigating hypotheses that are now well-established or understood as truth. These causal mechanisms are properties of the natural world, and thus are invariant conditions regardless of the collection domain or environment. We show in this paper how…

### Calibrationless Parallel MRI using Model based Deep Learning (C-MODL). (arXiv:1911.12443v1 [cs.LG])

We introduce a fast model based deep learning approach for calibrationless parallel MRI reconstruction. The proposed scheme is a non-linear generalization of structured low rank (SLR) methods that self learn linear annihilation filters from the same subject. It pre-learns non-linear annihilation relations in the Fourier domain from exemplar data. The pre-learning strategy significantly reduces the…

### QubitHD: A Stochastic Acceleration Method for HD Computing-Based Machine Learning. (arXiv:1911.12446v1 [cs.LG])

Machine Learning algorithms based on Brain-inspired Hyperdimensional (HD) computing imitate cognition by exploiting statistical properties of high-dimensional vector spaces. It is a promising solution for achieving high energy-efficiency in different machine learning tasks, such as classification, semi-supervised learning and clustering. A weakness of existing HD computing-based ML algorithms is the fact that they have to…

### On the choice of initial guesses for the Newton-Raphson algorithm. (arXiv:1911.12433v1 [math.NA])

The initialization of equation-based differential-algebraic system models, and more in general the solution of many engineering and scientific problems, require the solution of systems of nonlinear equations. Newton-Raphson’s method is widely used for this purpose; it is very efficient in the computation of the solution if the initial guess is close enough to it, but…

### Neumann Domains on Quantum Graphs. (arXiv:1911.12435v1 [math-ph])

The Neumann points of an eigenfunction $f$ on a quantum (metric) graph are the interior zeros of $f’$. The Neumann domains of $f$ are the subgraphs bounded by the Neumann points. Neumann points and Neumann domains are the counterparts of the well-studied nodal points and nodal domains. We prove some foundational results on Neumann domains…

### DC Optimal Power Flow with Joint Chance Constraints. (arXiv:1911.12439v1 [math.OC])

Managing uncertainty and variability in power injections has become a major concern for power system operators due to the increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a joint chance-constrained formulation of the DC optimal power flow (OPF) problem, which satisfies \emph{all} the constraints \emph{jointly} with a…

### A New Inventory Control Approach For Considering Customer Classes In An Integrated Supply Chain Management. (arXiv:1911.12442v1 [math.OC])

Supply chain management is an integrated approach for planning and controlling materials, information, and finances as they move in a process which begins from suppliers and ends with customers in forward approach. As distribution network planning is strategically done, the related decisions should be optimized. This supply chain planning involves transportation, the location of facilities,…

### Integral equalities and inequalities: a proxy-measure for multivariate sensitivity analysis. (arXiv:1911.12444v1 [math.PR])

Weighted Poincar\’e-type and related inequalities provide upper bounds of the variance of functions. Their application in sensitivity analysis allows for quickly identifying the active inputs. Although the efficiency in prioritizing inputs depends on the upper bounds, the latter can be big, and therefore useless in practice. In this paper, an optimal weighted Poincar\’e-type inequality and…

### Counting stationary points of the loss function in the simplest constrained least-square optimization. (arXiv:1911.12452v1 [math.PR])

We use Kac-Rice method to analyze statistical features of an “optimization landscape” of the loss function in a random version of the Oblique Procrustes Problem, one of the simplest optimization problems of the least-square type on a sphere.

### Reduction of Qubits in Quantum Algorithm for Monte Carlo Simulation by Pseudo-random Number Generator. (arXiv:1911.12469v1 [quant-ph])

It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random numbers are required to obtain one sample value…