Some philosophers - such as Popper and Kuhn - have cited the theory-shift from Newtonian to Einsteinian physics as one of the great scientific revolutions. This thesis argues against this that the shift was 'evolutionary' and exhibits a high degree of continuity (or quasi-continuity). I will develop a view that selects the relationships between events - one specified by dynamical laws at issue - as the essential elements within these two physical theoretical frameworks. This view brings together the dynamical perspective of space-time (developed by Harvey Brown, Robert DiSalle and Nick Huggett) and structuralism (developed by Henri Poincare and Pierre Duhem, and more recently resuscitated by John Worrall). The former view turns our attention away from the structure of space-time to the dynamical laws. While the second view will clarify to what extent the theory-change is evolutionary. The thesis consists of five chapters. The first chapter discusses the failures of existing views on the theory-change. The second chapter develops my own positive view - building, as indicated, on the work of the two aforementioned perspectives. The third and fourth chapters consider detailed aspects of the particular theory-change from Newtonian to Einsteinian physics from the point of view. The final chapter discusses the strengths of my view in comparison to the existing accounts of the theory-change.

The thesis deals with issues in the foundations of quantum mechanics, having to do with configuration space, the physical reality of quantum waves, additive conservation and EPR experiments. After a historical sketch of optical theories, concentrating on the dual nature of light, the passage from Hamilton's optico-mechanical analogy to wave mechanics is looked at. The wave-particle duality of de Broglie's theorie de la double solution is favoured after comparison with some of Schrodinger's views. Three experiments are considered which support that realist duality by indicating corpuscular and undulatory properties. If wave and particle coexist and the wave guides the particle along its trajectory, the wave must have a physical reality. The issue is whether such a wave can propagate in a fictitious configuration space. Features of quantum-mechanical interference are represented on the Riemann sphere. The treatment is generalized to infinite dimensions and then to tensor product spaces. 'Entanglement' is defined; certain states of composite systems cannot be broken up in such a way that every subsystem has a (pure) state. Entanglement is shown to be always empirically visible in principle; for every entangled state there exists a 'sensitive' observable which can tell apart from any mixture of factorizable states. Observables represented by functions of tensor products of operators cannot, however, tell the difference. Additive conservation is considered separately from interference, and is related to Schmidt's theorem and Bertlmann's socks in cases involving two subsystems. The treatment is then generalized to N subsystems. Interference and additive conservation are combined in two examples; the violation of Bell's inequality, and the theorem of Wigner, Araki and Yanase. Schrodinger's cat is made to 'oscillate.' Interpretations of quantum waves in configuration space are assessed and Furry's hypothesis discarded. The distinction is drawn between weak Bell inequalities deduced from local realism alone, and strong inequalities which involve physically unreasonable additional assumptions. It is shown that, as long as inefficient detectors are employed, photons can only be used to violate strong inequalities. Kaons are almost always detected and can be used to discriminate between quantum mechanics and local realism, and determine whether quantum waves really propagate in configuration space.

Throughout this thesis we test some aspects of the Standard Model (SM) at future high energy colliders. We start by examining the SU(2)x U(l) non-abelian nature of the SM. We consider the effect of anomalous couplings on the reaction e(^+)e(^-) → W(^+)W-γ, at s = 200 GeV, where the photon is soft. We show that the dependence on the anomalous couplings is of the same order as, but different from, the dependence of the leading order e(^+)e(^-) → W(^+)W(^-) cross section. We therefore argue that the two processes are complementary in providing precision tests of the Standard Model electroweak vertices. We also study the same process, e(^+)e(^-) → W(^+)W(^-)γ, at high-energy e(^+)e(^-) colliders to investigate the effect of genuine quartic W(^+)W(^-)γγ and W(^+)W(^-)Zγ anomalous couplings on the cross section. Deviations from the Standard Model predictions are quantified. We show how bounds on the anomalous couplings can be improved by choosing specific initial state helicity combinations. The dependence of the anomalous contributions on the collider energy is studied. We then proceed to present a detailed analysis of soft photon radiation in e(^+)e(^-) → tt → bW(^+)bW(^-). The radiation pattern is shown to depend sensitively on the top mass, width and energy, as well as the relative orientation of the initial and final state particles. Optimum conditions in which initial state radiation is minimised and the radiation pattern has the richest structure are discussed. Finally, the Higgs sector of the SM is visited, where the production of the SM Higgs ø with intermediate mass at the proposed CERN LEPOLHC ep collider in γq(q) → W(^±)øq’(q), γq(q) → Zºøq(q) and gγ → qqø events is studied. This is done for all possible (massive) flavours of the quarks q(q') and using photons generated via Compton back-scattering of laser light. We study signatures in which the Higgs decays to bb-pairs and the electroweak vector bosons W(^±) and Zº decay either hadronically or leptonically. All possible backgrounds to these signals are also computed.

The AdS/CFT correspondence provides a microscopic description of black hole thermodynamics. In this thesis, I study the relation between the classical physics of black holes and this microscopic description. I first consider the gauge theory's holographic encoding of non-trivial global causal structure, by studying various probes of the black hole. I study the charged black hole, so that the thermal scale is separated from the horizon scale, to demonstrate which relates to the field theory scale size. I find that, when probing the horizon, both Wilson loops and the duals of static supergavity probes have a scale size determined by the horizon, but the field theory scale size is divergent for a time-dependent probe. I also use the bulk black hole geometry to study the physics of the boundary theory. If we consider a dynamical boundary, a braneworld cosmology is induced from the bulk. However, the presence of matter on the brane introduces unconventional quadratic terms in the FRW equations of this braneworld. I find that bulk black holes induce identical unconventional terms on a matterless brane, therefore providing an alternative description of the same cosmology. A new conjecture relating classical and thermodynamic stability of black branes has emerged from the AdS/CFT correspondence. I make progress in proving this for the case of Schwarzschild black holes in a finite cavity. I also extend the conjecture to the supergravity backgrounds of the direct product form Schwarzschild-AdS x Sphere, which are relevant to my study of the AdS/CFT correspondence.

Oscillating solitonic solutions, the breathers, of affine Toda theory are studied. These breather solutions are constructed from two solitons of the same mass with velocity opposite of each other; by analytically continuing its velocity or rapidity to a complex value, the resulting solution becomes a periodic solution. Generally, the parameters in the soliton solutions are restricted to a certain range of definition. In particular, it is shown for a(^(1))(_n) and d(^(1))(_4) cases, these restrictions can be calculated explicitly. To some cases of a(^(a))(_n) theories, one can show that there are sine-Gordon embedded solitons which give rise to a sine-Gordon breather. Furthermore, these breather solutions carry topological charges. These topological charges are calculated and it is found that they are exactly the same as the topological charges of some single soliton cases. Moreover, for the non-zero topological charges, one can show they belong to the irreducible fundamental representation component of the tensor product of two fundamental representations associated with the constituent solitons. This Clebsch-Gordan decomposition property is in agreement with the fusing rule of soliton which in turn is similar to the fusing rule of the fundamental Toda particles. One can also make a conjecture that the zero topological charge is always carried by a breather whose constituent solitons are associated with either conjugate or self-conjugate fundamental representations. Although it is not possible to know the individual topological charge carried by the constituent solitons in a breather, nevertheless using the crossing symmetry similar to that of the crossing symmetry of the S'-matrix, one can perform a superficial calculation to determine the constituent soliton's topological charges. Attempts to understand the exact scattering matrices of the sine-Gordon solitons and breathers from a root space point of . view is also discussed. This study tries to mimic the exact S-matrix construction of the real coupling regime affine Toda theory from the root space by Dorey. In this study, one replaces the ordinary Coxeter element, which plays an important role in the real coupling regime, with other transformations to incorporate the infinite product nature of the sine-Gordon soliton scattering matrix. However, the desired consistent construction seems to elude the author in this study.

In this thesis we present research that extends our knowledge of the AdS/CFT correspondence; in particular we look at various non-supersymmetric Spacetimes and their conjectured dual field theory states. We consider known U(l) xU(l) invariant spaces and investigate the requirements for smoothness, which results in the construction of new smooth non-supersymmetric soliton solutions with Dl, D5 and momentum charges. We are able to identify dual states for these geometries in the field theory describing D1-D5 systems. Also discussed are interesting aspects of these Spacetimes and new orbifold solutions which are valid string backgrounds. In addition to this, we study time-dependent Spacetimes which are asymptotically locally anti-de Sitter. There are two different Spacetimes with the same asymptotics: the 'bubble of nothing' solutions and higher dimensional BTZ black holes, which are both asymptotically locally anti de Sitter and whose conformal boundaries are both conformal to de Sitter space times a circle. We use the AdS/CFT correspondence to give a description of the spacetimes in the dual field theory. We are also able to relate horizons and their thermodynamic quantities in the bulk and boundary spacetimes and are able to assign entropy to non-compact horizons.

In a time when large amounts of data about social, economical, technological, and biological systems are produced in a daily bases, complex networks have become a powerful tool to represent the structure of complex systems. The advances in complex networks research have been geared towards the study of two main questions: what can we understand from a complex system by looking at its structure, and more importantly, what is the interplay between the topological and dynamical properties of complex systems. The aim of this dissertation is to review and introduce new tools and methods to measure topological and dynamical properties of complex networks. In particular, it covers two specific problems related with the two previously presented questions: the study of the community structure of complex networks, and the analysis of the dynamical properties of a communication process. The first part of the thesis is focused on the study of the community structure of complex networks, that is, how and why the nodes of the network tend to form groups in which they are highly interconnected. The understanding of this problem is key to characterize the internal organization of complex systems, obtaining better insights about the dynamical behavior of their components. In this part we present an exhaustive review of the community structure identification problem, explaining the limitations of the current existing methods, and we introduce a new method to extract the community structure based on the extremal optimization algorithm. We also present several improvements that increase the efficiency and accuracy of current community identification methods and an exhaustive benchmark of the results obtained when applying this new method to the standard network metrics. These results show that the extremal optimization method and its modifications are one of the fastest and most accurate options to identify the community structure of a network. The second part of the thesis is devoted to the study of some dynamical properties of communication processes over complex networks. Using a simple traffic model we analyze the changes observed on some properties when we introduce congestion in the network: the scaling of the fluctuations and the dynamical robustness. First, we present the scaling of the fluctuations in order to provide a large-scale dynamical characterization of the traffic flow. The idea is that there are a large number of real complex systems that show a scaling relation between the average flux and the variability of this flux. The understanding of the scaling relation presented in the dissertation will help us design better traffic models. And second, we study the dynamical robustness of the traffic, defined as the capability of maintaining the efficiency of the communication when we remove a fraction of nodes of the network. We show that there is a dynamical percolation threshold that splits the network due to the congestion before the topological percolation threshold.

No description available.

In this thesis I explore two pertinent avenues of the $AdS/CFT$ correspondence: the rich, pragmatic context of non-relatavistic holography and the story of holographic multiboundary wormholes and their relation to the profound interplay between bulk geometry and boundary entanglement. In chapter \ref{intro}, I introduce the $AdS/CFT$ correspondence and review the key ideas that motivate and underlie the work in subsequent chapters. In chapter \ref{schleq2} we consider the development of a holographic dictionary for asymptotically locally Schr{\"o}dinger spacetimes for $z < 2$ in a massive vector model in various spatial dimensions. We carry out a linearised analysis of bulk perturbations and identify the boundary data as sources and vevs for the dual stress-energy complex. We verify that a sensible asymptotic expansion of bulk perturbations in sub-leading powers of $r$ exists by expanding them in eigenvalues of the boundary dilatation operator. The third chapter extends the work of the Chapter \ref{schleq2} to the case with $z=2$ in the massive vector model, in various dimensions, where the additional lightlike direction is regarded as internal from the boundary point of view, qualitatively unlike the $z<2$ case. Chapter \ref{hot} considers the entanglement structure of states holographically dual to multiboundary wormholes in the high-temperature limit, in which the thermal scale associated to each boundary is much larger than the $AdS$ scale. We find that the entanglement structure in this limit is almost entirely bipartite in this regime. The fifth chapter investigates the extent to which the results of chapter \ref{hot} generalise to regions of small moduli. We utilise heuristic tensor network methods to construct tensor network models of multiboundary wormhole states built by sewing tensors to Coxeter tilings and their quotients. We find in several cases that we can construct holographic states representing multiboundary wormhole geometries for which the entanglement structure is mostly, or almost entirely bipartite.

In chapter one I begin by discussing the basic ideas of quantum field, theory (QFT). I provide a review of symmetries in physics and then move on to discuss the quark model. Chapter two is a review of lattice gauge theory with particular attention paid to lattice QCD. I begin by discussing lattice QCD and then discuss some of the associated problems. I move on to discuss gauge fields on the lattice along with free lattice fermions. I then use this to define the lattice QCD action. I conclude this chapter by discussing how to reproduce the correct continuum physics. Chapter three discusses the basic numerical techniques employed in lattice simulations. I review methods for putting particles onto the lattice and conclude with a discussion of how to fit the resulting data. Chapter four reviews symmetries of the QCD Lagrangian, various forms of symmetry breaking in physics, the PCAC relation, the Goldberger-Treiman relation and the spontaneous breakdown of the axial symmetry. I move on to discuss sigma models and arrive at a basic chiral perturbation theory.