by meyolyv
Published: November 22, 2022 (4 days ago)
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Gaussian 09 Rev D 01 Em64t Torre

We present a metric for Gaussian densities. Similar to the Bhattacharyya distance and the symmetric Kullback-Leibler divergence, the proposed metric reduces the difference between two Gaussians to the difference between their parameters. Based on the proposed metric we introduce a symmetric and positive semi-definite kernel between Gaussian densities. We illustrate the benefits of the proposed metric in two settings: (1) a supervised problem, where we learn a low-dimensional projection that maximizes the distance between Gaussians, and (2) an unsupervised problem on spectral clustering where the similarity between samples is measured with our proposed kernel.

Gaussian 09 allows programs to use a limited number of memory allocations . For example, memory can be allocated in the following ways. i) By using the $Memory allocation command, a certain amount of memory is reserved for a new segment. ii) By using the $Memory allocation command, memory can be allocated automatically by the computer in the standard way (e.g., by allocating pages of memory, and perhaps several multiples of pages at that). iii) By using the $Memory allocation command, a certain amount of memory is allocated automatically, and never recycled.

Gaussian 09, with its accelerated integration package, allows programs to speed up each cycle of the integration routine by assigning specific memory or memory locations to certain tasks. This is important for three reasons. First, because the machine has a limited amount of memory, the more memory that is used for an individual task, the fewer tasks it can perform. Second, an application that is effectively using the full memory of a computer system makes this computer system unable to perform other tasks. Third, after a certain amount of memory is allocated for an individual task, this task will take longer to complete.

None of the default command-line options are directly suitable for controlling the particle symmetries of a molecular system. gasinit permits the force fields to be generated for a molecular system as parameters independent from the gas-phase geometry. The force field parameters can be defined via standard GAUSSIAN input files. The parameterization of a molecule is a complex process that must be defined in such a way that it is independent from the geometry.
The conditional expectation with respect to a Gaussian field is a Gaussian field itself. The (univariate) expectation of a square is a function of the variance. We can compute the mean of a power of the variance, for example the variance of a power of a Gaussian. For example, the variance of a power of a Gaussian may be computed from the mean of a squared Gaussian.
The Hessian of the free energy (var = X’) is a positive-definite matrix. The diagonal entry of the Hessian is the variance of a squared Gaussian in one dimension. The upper diagonal entry of the Hessian is the correlation between two squared Gaussians in two dimensions.
Gaussian09 supports Python and MATLAB for most of the core routines. In addition, it provides functions for reading and writing files using a number of external application programming interfaces (API), and uses its own command-line interface for interfacing with the language of your choice, as well as any third-party packages that can be interfaced with Python or MATLAB.
With Gaussian 09, it is possible to run different types of experiments interactively in Matlab. Through this, the user can repeat the experiment several times (both in terms of variables and of configurations), and save the results and debug information at each time step along the simulation. Moreover, the save step can be performed interactively to get the most useful version of the simulation, and to save only this version for more detailed analyses.
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