The Hitchhiker's Guide to Nonlinear Filtering

Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We start our review of the theory on nonlinear filtering from the simplest `filtering' task we can think of, namely static Bayesian inference. From there we continue our journey through discrete-time models, which is usually encountered in machine learning, and generalize to and further emphasize continuous-time filtering theory. The idea of changing the probability measure connects and elucidates several aspects of the theory, such as the parallels between the discrete- and continuous-time problems and between different observation models. Furthermore, it gives insight into the construction of particle filtering algorithms. This tutorial is targeted at scientists and engineers and should serve as an introduction to the main ideas of nonlinear filtering, and as a segway to more advanced and specialized literature.Comment: 64 page

Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society

Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud \ud \ud KEYWORDS: Emergence of Life and Human Consciousness;\ud Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud \u

Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to nonassociativity. Our reflections keep wandering back to the $Brahmagupta$ $Fibonacc$ two square identity and then via the $Euler$ four square identity up to the $Degen$ $Ggraves$ $Cayley$ eight square identity. These glimpses of history incline and invite us to retell the story on how about one month after quaternions have been carved on the $Broughamian$ bridge octonions were discovered by $John$ $Thomas$ $Ggraves$, jurist and mathematician, a friend of $William$ $Rowan$ $Hamilton$. As for today we just mention en passant quaternionic and octonionic quantum mechanics, generalization of $Cauchy$ $Riemann$ equations for octonions and triality principle and $G_2$ group in spinor language in a descriptive way in order not to daunt non specialists. Relation to finite geometries is recalled and the links to the 7stones of seven sphere, seven imaginary octonions units in out of the $Plato$ cave reality applications are appointed . This way we are welcomed back to primary ideas of $Heisenberg$, $Wheeler$ and other distinguished fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure

The Evolution of Homochirality

It is possible to reconsider the origin of biological homochirality in a novel way by formally invoking the standard groupoid approach to stereochemistry in a thermodynamic context that generalizes Landau's spontaneous symmetry breaking arguments. On Earth, limited metabolic free energy may have served as a low temperature analog to 'freeze' the system in the lowest energy state, i.e., the set of simplest homochiral transitive groupoids representing reproductive chemistries. These engaged in a Darwinian competition until a single configuration survived. Subsequent path dependent evolutionary process locked in this initial condition, in spite of increases in available metabolic free energy. Astrobiological outcomes, given higher initial metabolic free energy densities, could well be considerably richer, for example, of mixed chirality. One result would be a complicated distribution of biological chirality across a statistically large sample of extraterrestrial stereochemisty, in marked contrast with published predictions of a racemic average

Introduction and Acceptance of a Classical Charge Fiber Model (CFM) of Elementary Particles Evaluated by Means of an Online Tutorial-Based Survey

The introduction of a new classical model of elementary particles by Lucas and Bergman is studied using an online survey instrument. The model is based on finite-size, elastic, charged particles that take the form of charge fibers. The Charge Fiber Model of Elementary Particles (CFM) constitutes a fundamental departure from the current paradigm of Quantum Mechanics (QM) and the Standard Model (SM) of elementary particles. The survey familiarizes respondents with the basic principles and claims of the new model by means of an online tutorial, and queries respondents to gage their knowledge and opinion of the model (http://www.commonsensescience.org/survey). The analysis of the survey describes how experts in the field, or at least those who took the time to respond, regard the original and sweeping claims of the CFM. The response rate varied from a very low of 1.1% to a high of 29% among diverse scientific communities. This paper does not endorse the model, but considers the broader issue of how a theory representing a major departure from the status quo may be disseminated, perceived and accepted (or rejected) during its early stages. These issues are relevant to the ongoing development of a comprehensive young-earth creation model whose proponents, even with solid scientific and academic credentials, face a continuous struggle against the accepted scientific positions on origins, evolution and the age of the earth. Recognizing that scientific paradigms change over time provides incentive to evaluate models on the basis of their usefulness and to articulate our opinions of them in a manner that is both effective and nonoffensive

Gravity is a quantum force

The General Relativity understands gravity like inertial movement of the free fall of the bodies in curved spacetime of Lorentz. The law of inertia of Newton would be particular case of the inertial movement of the bodies in the spacetime flat of Euclid. But, in the step, from general to particular, breaks the law of inertia of Galilei since recovers apparently the rectilinear uniform movement but not the repose state, unless the bodies have undergone their collapse, although, the curved spacetime becomes flat and the curved geodesies becomes straight lines. For General Relativity is a natural law, within of a gravitational field, the accelerated movement of the bodies, that leads to that a geometric curvature puts out to the bodies in such geodesic movement. In this paper this error of General Relativity, like generalization of the law of inertia of Galilei, is examined and it is found that it is caused by suppression of mass and force that allows conceiving acceleration like property of spacetime. This is a mathematical and non-ontological result. Indeed, mass and force are the fundament that the gravitational acceleration is independent of the magnitude of mass of the bodies but gravity not of the mass and the gravitational force. The action of the gravity force, on inertial and gravitational masses of a body, produces mutual cancellation during its free fallen but too its weight when this cease. By means of the third law of Newton it shows that gravity is a force since weight is caused by gravity