scholarly journals Faster stochastic trace estimation with a Chebyshev product identity

2021 ◽  
Vol 120 ◽  
pp. 107246
Author(s):  
Eric Hallman
Keyword(s):  
Product Identity ◽  
Trace Estimation

scholarly journals Profile of Volatile Compounds of On-Farm Fermented and Dried Cocoa Beans Inoculated with Saccharomyces cerevisiae KY794742 and Pichia kudriavzevii KY794725

Molecules ◽  
2021 ◽  
Vol 26 (2) ◽  
pp. 344
Author(s):  
Gilson Celso Albuquerque Chagas Junior ◽  
Nelson Rosa Ferreira ◽  
Eloisa Helena de Aguiar Andrade ◽  
Lidiane Diniz do Nascimento ◽  
Francilia Campos de Siqueira ◽  
...  
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Volatile Compounds ◽  
Multivariate Analyses ◽  
High Capacity ◽  
Starter Cultures ◽  
Cocoa Beans ◽  
Pichia Kudriavzevii ◽  
Fermentative Capacity ◽  
Product Identity ◽  
On Farm

This study aimed to identify the volatile compounds in the fermented and dried cocoa beans conducted with three distinct inoculants of yeast species due to their high fermentative capacity: Saccharomyces cerevisiae, Pichia kudriavzevii, the mixture in equal proportions 1:1 of both species, and a control fermentation (with no inoculum application). Three starter cultures of yeasts, previously isolated and identified in cocoa fermentation in the municipality of Tomé-Açu, Pará state, Brazil. The seeds with pulp were removed manually and placed in wooden boxes for the fermentation process that lasted from 6 to 7 days. On the last day of fermentation, the almonds were packaged properly and placed to dry (36 °C), followed by preparation for the analysis of volatile compounds by GC-MS technique. In addition to the control fermentation, a high capacity for the formation of desirable compounds in chocolate by the inoculants with P. kudriavzevii was observed, which was confirmed through multivariate analyses, classifying these almonds with the highest content of aldehydes, esters, ketones and alcohols and low concentration of off-flavours. We conclude that the addition of mixed culture starter can be an excellent alternative for cocoa producers, suggesting obtaining cocoa beans with desirable characteristics for chocolate production, as well as creating a product identity for the producing region.

Shifted extended global Lanczos processes for trace estimation with application to network analysis

CALCOLO ◽  
2021 ◽  
Vol 58 (1) ◽  
Author(s):  
A. H. Bentbib ◽  
M. El Ghomari ◽  
K. Jbilou ◽  
L. Reichel
Keyword(s):  
Network Analysis ◽  
Trace Estimation

scholarly journals On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

2021 ◽  
Author(s):  
Alice Cortinovis ◽  
Daniel Kressner
Keyword(s):  
Large Scale ◽  
Gaussian Process Regression ◽  
Likelihood Estimation ◽  
Random Vectors ◽  
Symmetric Positive Definite ◽  
Matrix Logarithm ◽  
The Matrix ◽  
Trace Estimation ◽  
Scale Matrix ◽  
Existing Result

AbstractRandomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of $$x^T Bx$$ x T B x for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number of applications give rise to indefinite B. Most notably, this is the case for log-determinant estimation, a task that features prominently in statistical learning, for instance in maximum likelihood estimation for Gaussian process regression. The analysis of randomized trace estimates, including tail bounds, has mostly focused on the SPD case. In this work, we derive new tail bounds for randomized trace estimates applied to indefinite B with Rademacher or Gaussian random vectors. These bounds significantly improve existing results for indefinite B, reducing the number of required samples by a factor n or even more, where n is the size of B. Even for an SPD matrix, our work improves an existing result by Roosta-Khorasani and Ascher (Found Comput Math, 15(5):1187–1212, 2015) for Rademacher vectors. This work also analyzes the combination of randomized trace estimates with the Lanczos method for approximating the trace of f(B). Particular attention is paid to the matrix logarithm, which is needed for log-determinant estimation. We improve and extend an existing result, to not only cover Rademacher but also Gaussian random vectors.

scholarly journals Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product

2022 ◽  
Vol Volume 44 - Special... ◽  
Author(s):  
Liuquan Wang
Keyword(s):  
Analogous Result ◽  
Triple Product ◽  
Combinatorial Proof ◽  
Jacobi’S Triple Product Identity ◽  
Product Identity ◽  
Pentagonal Number Theorem ◽  
Nonnegative Coefficients ◽  
Jacobi's Triple Product Identity

Andrews and Merca investigated a truncated version of Euler's pentagonal number theorem and showed that the coefficients of the truncated series are nonnegative. They also considered the truncated series arising from Jacobi's triple product identity, and they conjectured that its coefficients are nonnegative. This conjecture was posed by Guo and Zeng independently and confirmed by Mao and Yee using different approaches. In this paper, we provide a new combinatorial proof of their nonnegativity result related to Euler's pentagonal number theorem. Meanwhile, we find an analogous result for a truncated series arising from Jacobi's triple product identity in a different manner.

scholarly journals Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy

10.37236/1796 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
James A. Sellers ◽  
Andrew V. Sills ◽  
Gary L. Mullen
Keyword(s):  
Famous Theorem ◽  
Partition Identities ◽  
Product Identity ◽  
Powers Of 2 ◽  
Pentagonal Number Theorem ◽  
Series Product

In 1958, Richard Guy proved that the number of partitions of $n$ into odd parts greater than one equals the number of partitions of $n$ into distinct parts with no powers of 2 allowed, which is closely related to Euler's famous theorem that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We consider extensions of Guy's result, which naturally lead to a new algorithm for producing bijections between various equivalent partition ideals of order 1, as well as to two new infinite families of parity results which follow from Euler's Pentagonal Number Theorem and a well-known series-product identity of Jacobi.

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