Histogram filtering as a tool in variational Monte Carlo optimization

Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.

Niagara Symphony Orchestra fonds, 1926, 1948-1998, n.d.

In 1948, The St. Catharines Civic Orchestra was founded by Jan Wolanek who was also the first conductor. Initially, this was a community orchestra and in 1963 its governing body assumed the name St. Catharines Symphony Association. In 1978 the name was again changed to The Niagara Symphony Association to reflect regional responsibilities. Wally Laughton was named Assistant Conductor in 1952/53. R.C. Clarke took over the orchestra for an interim period after Wolanek left in 1957. In 1958 Leonard Pearlman became the Music Director. It was under his direction that the Niagara Symphony Chorus came into existence in 1963. Milton Barnes succeeded Pearlman in 1964 and he was responsible for directing the symphony’s first opera production. He also made a concerted effort to attract younger people to symphonic music. In 1972 Leonard Atherton became the Music Director. He started the Cantata Choir and the Madrigal Singers. It was under his tenure that the orchestra became professional. When Atherton left in 1980, there were three seasons of guest conductors, the most notable of these conductors was Uri Mayer. In 1981 James Vincent Fusco was appointed as composer in residence and in 1983 Ermanno Florio became the Music Director. He retained this position until 1995 when Michael Reason took over. Daniel Swift was appointed as Music Director and Conductor in 1999 and the Niagara Symphony Orchestra became the orchestr in residence at Brock University. Laura Thomas was appointed as Associate Conductor 1n 2004. Daniel Swift’s resignation in 2008 began a search for a new Music Director. Bradley Thachuck was appointed as Music Director Designate and Principal Conductor in 2010. The orchestra is a fully professional, charitable institution with 52 members.The orchestra has also been led by Victor Feldbrill and Howard Cable. A junior symphony was first formed under Leonard Pearlman in 1960/61, but it wasn’t until 1965 that The St. Catharines Youth Orchestra was founded. The orchestra has consistently been an award winner in music festivals. The musicians range in age from 12 to 18 years. The highlight of the 1973-74 season was the orchestra’s participation in the first Canadian Festival of Youth Orchestras at The Banff School of Fine Arts. The St. Catharines Youth Orchestra has evolved from the St. Catharines School String and Brass Ensembles to a full scale symphony under the direction of conductor Paul van Dongen. In 1974 the Symphony House music program came into existence. It was 1976 when Richard Grymonpre was hired as the principal violinist of the St. Catharines Symphony Orchestra and conductor of the St. Catharines Youth Orchestra. Tak Ng Lai took over the position as conductor in 1978. Laura Thomas is currently the Music Director of The Niagara Youth Orchestra. Source: Niagara Symphony, Orchestra in Residence, Brock University website and notes from Niagara Symphony files

Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.