Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

This chapter introduces the subject of statistical pattern recognition (SPR). It starts by considering how features are defined and emphasizes that the nearest neighbor algorithm achieves error rates comparable with those of an ideal Bayes’ classifier. The concepts of an optimal number of features, representativeness of the training data, and the need to avoid overfitting to the training data are stressed. The chapter shows that methods such as the support vector machine and artificial neural networks are subject to these same training limitations, although each has its advantages. For neural networks, the multilayer perceptron architecture and back-propagation algorithm are described. The chapter distinguishes between supervised and unsupervised learning, demonstrating the advantages of the latter and showing how methods such as clustering and principal components analysis fit into the SPR framework. The chapter also defines the receiver operating characteristic, which allows an optimum balance between false positives and false negatives to be achieved.

Statistical Pattern Recognition

In the context of quantifying entanglement we study those functions of a multipartite state which do not increase under the set of local transformations. A mathematical characterization of these monotone magnitudes is presented. They are then related to optimal strategies of conversion of shared states. More detailed results are presented for pure states of bipartite systems. It is show that more than one measure are required simultaneously in order to quantify completely the non-local resources contained in a bipartite pure state, while examining how this fact does not hold in the so-called asymptotic limit. Finally, monotonicity under local transformations is proposed as the only natural requirement for measures of entanglement.

On the characterization of entanglement

General Instructions Write your CANDIDATE NUMBER clearly on each of the THREE answer books provided. If an electronic calculator is used, write its serial number in the box at the top right hand corner of the front cover of each answer book. USE ONE ANSWER BOOK FOR EACH QUESTION. Enter the number of each question attempted in the horizontal box on the front cover of its corresponding answer book. Hand in THREE answer books even if they have not all been used. You are reminded that the Examiners attach great importance to legibility, accuracy and clarity of expression.

Foundations of Quantum Mechanics

https://people.unica.it/giuseppesergioli/files/2012/04/26.-Fuzzy-approach-for-Toffoli-gate-with-mixed-states.pdf

Fuzzy Approach for Toffoli Gate in Quantum Computation With Mixed States

"On some properties of quasi-Mv algebras and &#8730;&#8242; quasi-Mv algebras"

We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to this problem by appealing to the completeness property of the majorization lattice. We give a proof of this property that relies heavily on the more geometric construction provided by the Lorenz curves, which allows to explicitly obtain the corresponding infimum and supremum. Our framework includes the case of possibly non-denumerable sets of target states (i.e. targets sets described by continuous parameters). In addition, we show that a notion of approximate majorization, which has recently found application in quantum thermodynamics, is in close relation with the completeness of this lattice. Finally, we provide some examples of optimal common resources within the resource theory of quantum coherence.

Optimal common resource in majorization-based resource theories

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

/pdf/quantum-mechanics-and-the-interpretation-of-the-orthomodular-2u2l4v0whp.pdf

Hector Freytes

Papers

Fuzzy Approach for Toffoli Gate in Quantum Computation With Mixed States

"On some properties of quasi-Mv algebras and √′ quasi-Mv algebras"

Optimal common resource in majorization-based resource theories

Quantum mechanics and the interpretation of the orthomodular square of opposition

On some properties of quasi MV algebras and square root quasi MV algebras. Part III.

Hector Freytes

Papers

Fuzzy Approach for Toffoli Gate in Quantum Computation With Mixed States

"On some properties of quasi-Mv algebras and &#8730;&#8242; quasi-Mv algebras"

Optimal common resource in majorization-based resource theories

Quantum mechanics and the interpretation of the orthomodular square of opposition

On some properties of quasi MV algebras and square root quasi MV algebras. Part III.

"On some properties of quasi-Mv algebras and √′ quasi-Mv algebras"