Cosmological Landscape From Nothing: Some Like It Hot

We suggest a novel picture of the quantum Universe -- its creation is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed state which is shown to be dynamically more preferable than the pure quantum state of the Hartle-Hawking type. The latter is dynamically suppressed by the infinitely large positive action of its instanton, generated by the conformal anomaly of quantum fields within the cosmological bootstrap (the self-consistent back reaction of hot matter). This bootstrap suggests a solution to the problem of boundedness of the on-shell cosmological action and eliminates the infrared catastrophe of small cosmological constant in Euclidean quantum gravity. The cosmological landscape turns out to be limited to a bounded range of the cosmological constant $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The domain $\Lambda<\Lambda_{\rm min}$ is ruled out by the back reaction effect which we analyze by solving effective Euclidean equations of motion. The upper cutoff is enforced by the quantum effects of vacuum energy and the conformal anomaly mediated by a special ghost-avoidance renormalization of the effective action. They establish a new quantum scale $\Lambda_{\rm max}$ which is determined by the coefficient of the topological Gauss-Bonnet term in the conformal anomaly. This scale is realized as the upper bound -- the limiting point of an infinite sequence of garland-type instantons which constitute the full cosmological landscape. The dependence of the cosmological constant range on particle phenomenology suggests a possible dynamical selection mechanism for the landscape of string vacua.Comment: Final version, to appear in JCA

Programmable Insight: A Computational Methodology to Explore Online News Use of Frames

abstract: The Internet is a major source of online news content. Online news is a form of large-scale narrative text with rich, complex contents that embed deep meanings (facts, strategic communication frames, and biases) for shaping and transitioning standards, values, attitudes, and beliefs of the masses. Currently, this body of narrative text remains untapped due—in large part—to human limitations. The human ability to comprehend rich text and extract hidden meanings is far superior to known computational algorithms but remains unscalable. In this research, computational treatment is given to online news framing for exposing a deeper level of expressivity coined “double subjectivity” as characterized by its cumulative amplification effects. A visual language is offered for extracting spatial and temporal dynamics of double subjectivity that may give insight into social influence about critical issues, such as environmental, economic, or political discourse. This research offers benefits of 1) scalability for processing hidden meanings in big data and 2) visibility of the entire network dynamics over time and space to give users insight into the current status and future trends of mass communication.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Diversity, variability and persistence elements for a non-equilibrium theory of eco-evolutionary dynamics

Natural ecosystems persist in variable environments by virtue of a suite of traits that span from the individual to the community, and from the ecological to the evolutionary scenarios. How these internal characteristics operate to allow living beings to cope with the uncertainty present in their environments is the subject matter of quantitative theoretical ecology. Under the framework of structural realism, the present dissertation project has advocated for the strategy of mathematical modeling as a strategy of abstraction. The goal is to explore if a range of natural ecosystems display the features of complex systems, and evaluate whether these features provide insights into how they persist in their current environments, and how might they cope with changing environments in the future. A suite of inverse, linear and non-linear dynamical mathematical models, including non-equilibrium catastrophe models, and structured demographic approaches is applied to five case studies of natural systems fluctuating in the long-term in diverse scenarios: phytoplankton in the global ocean, a mixotrophic plankton food web in a marine coastal environment, a wintering waterfowl community in a major Mediterranean biodiversity hot-spot, a breeding colony of a keystone avian scavenger in a mountainous environment and the shorebird community inhabiting the coast of UK. In all case studies, there is strong evidence that ecosystems are able to closely track their common environment through several strategies. For example, in global phytoplankton communities, a latitudinal gradient in the positive impact of functional diversity on community stability counteracts the increasing environmental variability with latitude. Mixotrophy, by linking several feeding strategies in a food web, internally drives community dynamics to the edge of instability while maximizing network complexity. In contrast, an externally generated major perturbation, operating through planetary climatic disruptions, induce an abrupt regime shift between alternative stable states in the wintering waterfowl community. Overall, the natural systems studied are shown to posses features of complex systems: connectivity, autonomy, emergence, non-equilibrium, non-linearity, self-organization and coevolution. In rapidly changing environments, these features are hypothesized to allow natural system to robustly respond to stress and disturbances to a large extent. At the same time, future scenarios will be probably characterized by conditions never experienced before by the studied systems. How will they respond to them, is an open question. Based on the results of this dissertation, future research directions in theoretical quantitative ecology will likely benefit from non-autonomous dynamical system approaches, where model parameters are a function of time, and from the deeper exploration of global attractors and the non-equilibriumness of dynamical systems

Path Integrals in the Sky: Classical and Quantum Problems with Minimal Assumptions

Cosmology has, after the formulation of general relativity, been transformed from a branch of philosophy into an active field in physics. Notwithstanding the significant improvements in our understanding of our Universe, there are still many open questions on both its early and late time evolution. In this thesis, we investigate a range of problems in classical and quantum cosmology, using advanced mathematical tools, and making only minimal assumptions. In particular, we apply Picard-Lefschetz theory, catastrophe theory, infinite dimensional measure theory, and weak-value theory. To study the beginning of the Universe in quantum cosmology, we apply Picard-Lefschetz theory to the Lorentzian path integral for gravity. We analyze both the Hartle-Hawking no-boundary proposal and Vilenkin's tunneling proposal, and demonstrate that the Lorentzian path integral corresponding to the mini-superspace formulation of the two proposals is well-defined. However, when including fluctuations, we show that the path integral predicts the existence of large fluctuations. This indicates that the Universe cannot have had a smooth beginning in Euclidean de Sitter space. In response to these conclusions, the scientific community has made a series of adapted formulations of the no-boundary and tunneling proposals. We show that these new proposals suffer from similar issues. Second, we generalize the weak-value interpretation of quantum mechanics to relativistic systems. We apply this formalism to a relativistic quantum particle in a constant electric field. We analyze the evolution of the relativistic particle in both the classical and the quantum regime and evaluate the back-reaction of the Schwinger effect on the electric field in $1+1$-dimensional spacetime, using analytical methods. In addition, we develop a numerical method to evaluate both the wavefunction and the corresponding weak-values in more general electric and magnetic fields. We conclude the quantum part of this thesis with a chapter on Lorentzian path integrals. We propose a new definition of the real-time path integral in terms of Brownian motion on the Lefschetz thimble of the theory. We prove the existence of a $\sigma$-measure for the path integral of the non-relativistic free particle, the (inverted) harmonic oscillator, and the relativistic particle in a range of potentials. We also describe how this proposal extends to more general path integrals. In the classical part of this thesis, we analyze two problems in late-time cosmology. Multi-dimensional oscillatory integrals are prevalent in physics, but notoriously difficult to evaluate. We develop a new numerical method, based on multi-dimensional Picard-Lefschetz theory, for the evaluation of these integrals. The virtue of this method is that its efficiency increases when integrals become more oscillatory. The method is applied to interference patterns of lensed images near caustics described by catastrophe theory. This analysis can help us understand the lensing of astrophysical sources by plasma lenses, which is especially relevant in light of the proposed lensing mechanism for fast radio bursts. Finally, we analyze large-scale structure formation in terms of catastrophe theory. We show that the geometric structure of the three-dimensional cosmic-web is determined by both the eigenvalue and the eigenvector fields of the deformation tensor. We formulate caustic conditions, classifying caustics using properties of these fields. When applied to the Zel'dovich approximation of structure formation, the caustic conditions enable us to construct a caustic skeleton of the three-dimensional cosmic-web in terms of the initial conditions

The decoded information from the Hc-4 molar in Equus stenonis requires renewing the Linnaeus paradigm

Owing to the uncertainties and anomalies that are historically constants in the Linnaean paradigm, it happens that the phylogenetic data obtained from crown molars, although these morphologies are inherited, have a complementary scientific value with regard to the biochemical data. The Hc¿4 molar (Betic Cordillera, Spain) is analyzed in order to obtain new data using two techniques. Its crown wear section is a biomineralized embryonic morphology (retrogerminative technique), and its enamel line draws hexagonal marks (superimposition technique). These data are the foundations of the mitosis area loop development hypothesis during morphogenesis. The tooth structure is a germination process of the embryonic dermal masses (mitosis areas), and in relationship to (1) the moment they were born during loop process, (2) size, and (3) location when they constitute a specific cusps crown when they are petrified by an enamel mantle. In conclusion, Linnaean characteristics (morphology) are associated with two parameters: frequency percentage with which the cusps are inherited and their functional role. This parameters group is called ¿Biological Nature¿. The Reference Series in each molar is the biological nature values group positioned in linear order. The Reference Series of each linnaean holotype imply phylogenetic relationships using similarity percentages and the Linnaean uncertainties disappear from the phylogeny. If I express phenotype with the reference series and also the genotype (DNA) is displayed with a numerical sequence, then it happens that we have two numerical sequences and between them exist cause and effect relationshipPeer Reviewe

Quantifying degraded subtropical thicket structure and composition: a multi-scale approach in the Eastern Cape, South Africa

The loss in canopy cover from over-browsing severely degrades the ecological integrity of spekboom-dominated thicket in the Eastern Cape. A homogenisation of species across the landscape and high heterogeneity at fine scales has been reported with little evidence of recovery. As an interlinked consequence, the loss in important biological structures and composition impacts greatly on soil resources and therefore function. This thesis provides a baseline of degraded thicket abiotic and biotic structure and composition over both spatial and temporal scales within the Greater Addo Elephant National Park (GAENP), including Darlington, Kabouga and Addo Main and within the Baviaanskloof. The study aimed to find correlates of species composition within sites and assess changes in composition with degradation and recovery times. Across the GAENP, landscape degradation was most evident in post-1960 aerial imagery. The duration since sampled sites have been incorporated into the GAENP did not influence species composition, however the period of degradation and severity, did. Across the landscape, communities were strongly associated with each of the four sites and separated predominantly by rainfall, gravel and altitude. A total of 345 plant species were identified across the landscape and despite degradation, each site was characterised into three to five communities each, barring Baviaanskloof which had no significantly different communities. Across the landscape, matrix composition comprised predominantly of Pentzia incana, Drosanthemum hispidum, Galenia pubescens and Cynodon species. Woody cover within patches included smaller Grewia robusta, Rhigozum obovatum and Vachellia karroo and the larger Pappea capensis and Euclea undulata. The succulent shrub Euphorbia caerulescens in Darlington and succulent tree Aloe ferox in Baviaanskloof occurred abundantly as a consequence of degradation. Species richness was significantly correlated to patch size in all sites, but Kabouga had the greatest richness and probability of a suite of species occurring within a patch. Higher woody and succulent cover in Kabouga was therefore associated with higher soil C, root percentage and bulk density. Other sites were higher in Ca, Na, K and P. The method of degradation scoring was not sufficiently accurate and it is recommended that indicator species within the matrix should be used instead of growth forms. The findings of this thesis are conceptualised within a double-cusped catastrophe model and recommendations for restoration are provided

Sudden change, society and urban form

Rapid changes in the environment create situations which man has never previously experienced or anticipated. Situations such as social revolutions, migrations to new places, or disasters often require that society re- organises itself in a short period of time, breaks the continuity with its past and reaches a new state of stability. This re- organisation is responsible for the emergence of a whole series of psychological and social effects. The main objective of this study is to explain the nature of the changes in urban form which occur in such situations.One of the major assertions of this thesis is that continuity is an inner characteristic of the self- It is one characteristic of the temporal dimension of life and not a reflection of a continuity in the spatial dimension. Therefore, the contribution of the designer is to maintain the temporal continuity of cities while explaining the spatial transformations through models based on discontinuous behaviour.The cultural development and the physiological limitations of man to rapid change are taken as evidence in the demonstration of the extent of the problem. Within this context, radical change in the formation of the environment is shown to be are expression of the human mind and not the direct effect of changes in the environmental forces. For that reason, the effect of sudden change in the environment is studied in relation to the concept of time: the direction between past, present and future.As this assumption does not require any kind of spatial continuity, a model based on discontinuity is used to evaluate the transformation of cities in circumstances of rapid change

The deep structure of Gaussian scale space images

In order to be able to deal with the discrete nature of images in a continuous way, one can use results of the mathematical field of 'distribution theory'. Under almost trivial assumptions, like 'we know nothing', one ends up with convolving the image with a Gaussian filter. In this manner scale is introduced by means of the filter's width. The ensemble of the image and its convolved versions at al scales is called a 'Gaussian scale space image'. The filter's main property is that the scale derivative equals the Laplacean of the spatial variables: it is the Greens function of the so-called Heat, or Diffusion, Equation. The investigation of the image all scales simultaneously is called 'deep structure'. In this thesis I focus on the behaviour of the elementary topological items 'spatial critical points' and 'iso-intensity manifolds'. The spatial critical points are traced over scale. Generically they are annihilated and sometimes created pair wise, involving extrema and saddles. The locations of these so-called 'catastrophe events' are calculated with sub-pixel precision. Regarded in the scale space image, these spatial critical points form one-dimensional manifolds, the so-called critical curves. A second type of critical points is formed by the scale space saddles. They are the only possible critical points in the scale space image. At these points the iso-intensity manifolds exhibit special behaviour: they consist of two touching parts, of which one intersects an extremum that is part of the critical curve containing the scale space saddle. This part of the manifold uniquely assigns an area in scale space to this extremum. The remaining part uniquely assigns it to 'other structure'. Since this can be repeated, automatically an algorithm is obtained that reveals the 'hidden' structure present in the scale space image. This topological structure can be hierarchically presented as a binary tree, enabling one to (de-)select parts of it, sweeping out parts, simplify, etc. This structure can easily be projected to the initial image resulting in an uncommitted 'pre-segmentation': a segmentation of the image based on the topological properties without any user-defined parameters or whatsoever. Investigation of non-generic catastrophes shows that symmetries can easily be dealt with. Furthermore, the appearance of creations is shown to be nothing but (instable) protuberances at critical curves. There is also biological inspiration for using a Gaussian scale space, since the visual system seems to use Gaussian-like filters: we are able of seeing and interpreting multi-scale