Software:
1. Real vs Quantism
is an interactive animation that simulates transitions between two
stationary states of the hydrogen atom. Continuous transitions of
Realism as well as discontinuous jumps of Quantism can be played. All
the papers on Realism mentioned below are bundled in this software.
2. Crespin 2.0 Fast Perceptron Trainer, is a freeware that calculates architecture and weights of perceptron neural networks, runs under
Windows, has a graphical interface and provides control on the generalization capabilities of the networks it provides.
Papers on Realism:
The following five papers on Realism are also bundled with the Real vs Quantism
(RvsQ.exe) software package.
1. Realism:
A continuous, deterministic and chaotic wave theory of atoms based on
Schrödinger self-adjoint operator and the (realistic) flow it defines in the
space of Hilbert rays. No use is made of probabilistic interpretation, random
jumps, uncertainty principle, wave-particle duality or hidden variables.
Provides a considerable simplification of Quantism and has the same eigenvalues.
This down-to-earth theory furnishes a natural model of atomic phenomena in
agreement with experimental facts. 73 pages.
2. Projective
Dynamical Systems and Realism: Operators in Hilbert space define in
the associated projective space certain projective dynamical systems and an
observable. Systems defined by unitary and by self adjoint operators are
considered. Part I studies the finite dimensional cases and Part II discusses
infinite dimensional ones. The paper contains the Projective Spectral Theorem
(PST), a mathematical result relevant for Realism (see preprint above). PST is
to projective dynamics as the usual linear spectral theorem is to linear
dynamics. 47 pages.
3. An
Introduction to Realism: This elementary introduction to Realism
explains 2-level systems. The states, observables and evolution equation are
introduced as postulates for general systems and then applied in the 2-level
case. Assuming mild physical hypothesis (the Photon Hypothesis) it is shown in
detail how to deduce (and interpret) Einstein formula E=hc/(wavelength).
Designed mostly for students, results are worked out clearly and various figures
facilitate assimilation of new concepts. 32 pages.
4. Manifesto against
Quantism: A document that unveils the situation of Physics
with
regard to Quantism. Of interest for anyone interested in unmasking
Quantism and rationalizing Physics as well as other branches of Science
affected by
Quantum Theory. 2 pages.
5. FAQ Realism vs
Quantism: This paper was prepared to be used with (and is part of)
the Real vs Quantism software package. Discusses, in the FAQ question-answer
style, various basic issues concerning the replacement of Quantism by Realism.
The brief sections include:
Realism and Quantism
Change and Evolution
Mathematics of Evolution
Outline of Realism
Discussion of Realism
Sociology of Realism
History of Realism
Goals of Realism
Provides a critical view of Quantism and the desirable end of its crooked paradigms. 12 pages.
Papers on Neural Networks:
1. Neural
polyhedra: Explicit formulas to express any polyhedron as a three
layer perceptron neural network. Useful to calculate directly and without
training the architecture and weights of a network that executes a given pattern
recognition task. See preprint below. 8 pages.
2. Pattern recognition
with untrained perceptrons: Shows how to construct polyhedra
directly from given pattern recognition data. The perceptron network associated
to these polyhedra (see preprint above) solves the recognition problem. 10
pages.
3. Neural network
formalism: Neural networks are defined using only elementary
concepts from set theory, without the usual connectionistic graphs. The typical
neural diagrams are derived from these definitions. This approach provides
mathematical techniques and insight to develop theory and applications of neural
networks. 8 pages.
4. Geometry of
perceptrons: It is proved that semilinear perceptron networks are
products of characteristic maps of polyhedra. This gives insight into the
geometric structure of these networks. The result also holds for more general
(semialgebraic, etc.) perceptron networks, and suggests a new technique to solve
pattern recognition problems. See other preprints in this location and NEUROGON
software below. 3 pages.
5. Generalized
Backpropagation: Global backpropagation formulas for differentiable
neural networks are considered from the viewpoint of minimization of the
quadratic error using the gradient method. The gradient of (the quadratic error
function of) a processing unit is expressed in terms of the output error and the
transposed derivative of the unit with respect to the weight. The gradient of
the layer is the product of the gradients of the processing units. The gradient
of the network equals the product of the gradients of the layers.
Backpropagation provides the desired outputs or targets for the layers. Standard
formulas for semilinear networks are deduced as a special case. 14 pages.
6. A Primer on Perceptrons:
Basic vocabulary for perceptron neural networks with emphasis on
mathematical language. Assumes familiarity with vector spaces and
matrices. 7 pages.
Mail to: dcrespin@gmail.com
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