Intrinsic Information-Theoretic Models.

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions N (µ, σ0), as before, but with a constant σ0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution Nm(µ,Σ0) with a constant variance-covariance matrix Σ0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger's equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of σ0, altogether leading to the concept of "intrinsic". Similarly, as in our previous work with the estimator's variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the "intrinsic" Cramér-Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes' theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of "intrinsic" information-theoretic models, which are essential for developing physics.

Information-Theoretic Models for Physical Observables.

This work addresses J.A. Wheeler's critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space of a smooth statistical manifold of normal probability distributions. Following this approach, we study the stationary states with the time-independent Schrödinger's equation to discover that the information could be represented and distributed over a set of quantum harmonic oscillators, one for each independent source of data, whose coordinate for each oscillator is a parameter of the smooth statistical manifold to estimate. We observe that the estimator's variance equals the energy levels of the quantum harmonic oscillator, proving that the estimator's variance is definitively quantized, being the minimum variance at the minimum energy level of the oscillator. Interestingly, we demonstrate that quantum harmonic oscillators reach the Cramér-Rao lower bound on the estimator's variance at the lowest energy level. In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes' theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. Interestingly, the opposite is also true, as the prior is constant. Altogether, these results suggest that we can break the sources of information into little elements: quantum harmonic oscillators, with the square modulus of the collective mode at the lowest energy representing the most likely reality, supporting A. Zeilinger's recent statement that the world is not broken into physical but informational parts.

Discriminant analysis algorithm based on a distance function and on a Bayesian decision.

We propose a new algorithm for the allocation of an individual to one of several possible groups or populations. The algorithm enables us to define a finite partition over the sample space, based on distance function. This partition is used, jointly with the application of a standard Bayesian decision rule, to allocate individuals to the populations. The algorithm also provides a measure of the allocation confidence for each individual, in a similar manner to that of logistic regression. The error rates for classification are also computed using the leave-one-out method. Results are compared with those obtained with other discriminant analysis techniques previously reported: Fisher's linear discriminant function, the quadratic discriminant function, logistic discrimination, and others.

Spontaneous fracture of hypertrophied genial tubercles.

A case of spontaneous fracture of hypertrophied genial tubercles is reported. This is an uncommon event with only six previously reported cases. This entity is usually associated with severe edentulous bone resorption, a condition related to the pathogenesis of this fracture. Clinical complaints include painful swelling of the floor of the mouth and impaired tongue function. If left untreated, mucosal inflammatory changes may appear and a biopsy should be performed. Total recovery is obtained after removal of the fractured fragments.

Atypical histiocytic granuloma of the tongue: case report.

Primary malignant lymphomas of the tongue have rarely been described, and reported cases are usually related to the posterior part of the tongue which is rich in lymphoid tissue, forming part of Waldeyer's ring. Making a distinction between pseudolymphoma and malignant lymphoma is important. Pseudolymphoma is a benign lesion not requiring aggressive therapy. Several lesions in the oral cavity, including atypical histiocytic granuloma, angiolymphoid hyperplasia with eosinophilia, and traumatic ulcerative granuloma with stromal eosinophilia have been described as having certain microscopic features similar to those of pseudolymphoma. Atypical histiocytic granuloma is not associated with systemic disease or dissemination and heals spontaneously despite its microscopic appearance.

Optic nerve blindness following a malar fracture.

Optic nerve blindness following a malar fracture is an uncommon and usually permanent complication. When the loss of vision is immediate and total, the prognosis is poor. The case of a patient who suffered immediate and complete loss of vision after a malar fracture is presented. Computed tomography revealed compression of the optic nerve by bony fragments. No improvement was observed after megadose steroids and surgical treatment. The incidence, pathogenesis, diagnostic approach and therapeutic possibilities are discussed and the importance of establishing precisely the moment of the loss of vision is stressed.

[Morphometric study of epithelial neoplasms of the parotid gland]. / Estudio morfométrico de las neoplasias epiteliales de la glándula parótida.

The histological diagnosis of parotid gland tumoral pathology is difficult in some cases. Morphometry provides a possibility to quantify the histopathology minimizing the risk of a misdiagnosis. On this basis, a morphometric study of the normal parotid tissue and 13 types of parotid tumors is carried out and nuclear Area, D. Circle, Form. PE, and Form. AR are calculated. Statistical analysis the results is made using the Student's "t-test" and significant differences between benign and malignant tumors and between each tumor and the remainder are obtained. Contribution of the results to the histopathological diagnosis is discussed.