An arithmetic circuit or formula is multilinear if the polynomial computed at each of its wires is multilinear. We give an explicit polynomial f (x1, . . . ,xn) with coefficients in {0,1} such that over any field: 1. f can be computed by a polynomial-size multilinear circuit of depth O(log2 n). 2. Any multilinear formula for f is of size nΩ(logn). This gives a superpolynomial gap between multil...

In this note, we show that over fields of any characteristic, exponential sums of Boolean instantiations of polynomials computed by multilinear circuits can be computed by multilinear circuits with polynomial blow-up in size. In particular, multilinear-VNP equals multilinear-VP. Our result showing closure under exponential sums also holds for other restricted multilinear classes – polynomials c...

Only rarely have researchers attempted to mathematically model the complex interrelationships of variables within an electronic meeting. Here, we show how topic-related measures can be used by an artificial neural network to accurately forecast the number of relevant comments generated by each person in these automated meetings. In comparison, naïve and multilinear regression forecasts were sig...

This study showed not only aerosol source contributions based on a positive matrix factorization (PMF) analysis, but also mass scattering and absorption efficiencies (MSE and MAE) of different aerosol sources by using multilinear regression method at urban, regional and remote backgrounds in the Spain. Although the results and discussion were documented well, there are several important shortco...

This study showed not only aerosol source contributions based on a positive matrix factorization (PMF) analysis, but also mass scattering and absorption efficiencies (MSE and MAE) of different aerosol sources by using multilinear regression method at urban, regional and remote backgrounds in the Spain. Although the results and discussion were documented well, there are several important shortco...

An arithmetic circuit or formula is multilinear if the polynomial computed at each of its wires is multilinear. We give an explicit example for a polynomial f(x1, ..., xn), with coefficients in {0, 1}, such that over any field: 1. f can be computed by a polynomial-size multilinear circuit of depth O(log n). 2. Any multilinear formula for f is of size nΩ(logn). This gives a super-polynomial gap ...

The aim of this study was to develop a multiple linear regression (MLR) model predict the specific methane production (SMP) from dry anaerobic digestion (AD) organic fraction municipal solid waste (OFMSW). A data set an experimental test on pilot-scale plug-flow reactor (PFR) including 332 observations used build model. Pearson?s correlation matrix and principal component analysis (PCA) examine...

Abstract Food instability has been linked to infertility, health issues, accelerated aging, incorrect insulin regulation, and more. Innovative approaches increased food availability quality. Agriculture environment monitoring systems need IoT machine learning. sensors provide all necessary data for agriculture production forecast, fertilizer management, smart irrigation, crop monitoring, diseas...

We obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m-linear Fourier series. We formulate conditions for the convergence of multilinear series and we...