Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models we build to spatially extended cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.

Theoretical investigation of intra- and inter-cellular spatiotemporal calcium patterns in microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined.^ Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. ^ From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.^

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Spectral distortions of the cosmic microwave background and small-scale gravitational waves as new windows on the Early Universe

In this thesis, we explore constraints which can be put on the primordial power spectrum of curvature perturbations beyond the scales probed by anisotropies of the cosmic microwave background and galaxy surveys. We exploit present and future measurements of CMB spectral distortions, and their synergy with CMB anisotropies, as well existing and future upper limits on the stochastic background of gravitational waves. We derive for the first time phenomenological templates that fit small-scale bumps in the primordial power spectrum generated in multi-field models of inflation. By using such templates, we study for the first time imprints of primordial peaks on anisotropies and spectral distortions of the cosmic microwave background and we investigate their contribution to the stochastic background of gravitational waves. Through a Monte Carlo Markov Chain analysis we infer for the first time the constraints on the amplitude, the width and the location of such bumps using Planck and FIRAS data. We also forecast how a future spectrometer like PIXIE could improve FIRAS boundaries. The results derived in this thesis have implications for the possibility of primordial black holes from inflation.

Search for neutral higgs bosons in Multi-b-Jet events in pp̄ collisions at s=1.96TeV

Data recorded by the D0 experiment at the Fermilab Tevatron Collider are analyzed to search for neutral Higgs bosons produced in association with b quarks. This production mode can be enhanced in the minimal supersymmetric standard model (MSSM). The search is performed in the three b quark channel using multijet triggered events corresponding to an integrated luminosity of 1fb-1. No statistically significant excess of events with respect to the predicted background is observed and limits are set in the MSSM parameter space. © 2008 The American Physical Society.

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Higgs pair production at the LHC in models with universal extra dimensions

In this Letter we study the process of gluon fusion into a pair of Higgs bosons in a model with one universal extra dimension. We find that the contributions from the extra top quark Kaluza-Klem excitations lead to a Higgs pair production cross section at the LHC that can be significantly altered compared to the Standard Model value for small values of the compactification scale. (C) 2007 Elsevier B.V. All rights reserved.

CP properties of symmetry-constrained two-Higgs-doublet models

The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of all cases in the bilinear formalism. An exact symmetry implies CP conservation. We show that soft breaking of the symmetry can lead to spontaneous CP violation (CPV) in three of the classes.

Implications of the LHC two-photon signal for two-Higgs-doublet models

We study the implications for two-Higgs-doublet models of the recent announcement at the LHC giving a tantalizing hint for a Higgs boson of mass 125 GeV decaying into two photons. We require that the experimental result be within a factor of 2 of the theoretical standard model prediction, and analyze the type I and type II models as well as the lepton-specific and flipped models, subject to this requirement. It is assumed that there is no new physics other than two Higgs doublets. In all of the models, we display the allowed region of parameter space taking the recent LHC announcement at face value, and we analyze the W+W-, ZZ, (b) over barb, and tau(+)tau(-) expectations in these allowed regions. Throughout the entire range of parameter space allowed by the gamma gamma constraint, the numbers of events for Higgs decays into WW, ZZ, and b (b) over bar are not changed from the standard model by more than a factor of 2. In contrast, in the lepton-specific model, decays to tau(+)tau(-) are very sensitive across the entire gamma gamma-allowed region.

Models with three Higgs doublets in the triplet representations of A(4) or S-4

We consider the quark sector of theories containing three scalar SU(2)(L) doublets in the triplet representation of A(4) (or S-4) and three generations of quarks in arbitrary A(4) (or S-4) representations. We show that for all possible choices of quark field representations and for all possible alignments of the Higgs vacuum expectation values that can constitute global minima of the scalar potential, it is not possible to obtain simultaneously nonvanishing quark masses and a nonvanishing CP-violating phase in the Cabibbo-Kobayashi-Maskawa quark mixing matrix. As a result, in this minimal form, models with three scalar fields in the triplet representation of A(4) or S-4 cannot be extended to the quark sector in a way consistent with experiment. DOI: 10.1103/PhysRevD.87.055010.

Neutrino masses and mixing in A(4) models with three Higgs doublets

We study neutrino masses and mixing in the context of flavor models with A(4) symmetry, three scalar doublets in the triplet representation, and three lepton families. We show that there is no representation assignment that yields a dimension-5 mass operator consistent with experiment. We then consider a type-I seesaw with three heavy right-handed neutrinos, explaining in detail why it fails, and allowing us to show that agreement with the present neutrino oscillation data can be recovered with the inclusion of dimension-3 heavy neutrino mass terms that break softly the A(4) symmetry.

Stability of the tree-level vacuum in two Higgs doublet models against charge or CP spontaneous violation

We show that in two Higgs doublet models at tree-level the potential minimum preserving electric charge and CP symmetries, when it exists, is the global one. Furthermore, we derived a very simple condition, involving only the coefficients of the quartic terms of the potential, that guarantees spontaneous CP breaking. (C) 2004 Elsevier B.V. All rights reserved.

Could the LHC two-proton signal correspond to the heavier scalar in two-higgs-doublet models?

LHC has reported tantalizing hints for a Higgs boson of mass 125 GeV decaying into two photons. We focus on two-Higgs-doublet Models, and study the interesting possibility that the heavier scalar H has been seen, with the lightest scalar h having thus far escaped detection. Nonobservation of h at LEP severely constrains the parameter-space of two-Higgs-doublet models. We analyze cases where the decay H -> hh is kinematically allowed, and cases where it is not, in the context of type I, type II, lepton-specific, and flipped models.

Theory and phenomenology of two-higgs-doublet models

We discuss theoretical and phenomenological aspects of two-Higgs-doublet extensions of the Standard Model. In general, these extensions have scalar mediated flavour changing neutral currents which are strongly constrained by experiment. Various strategies are discussed to control these flavour changing scalar currents and their phenomenological consequences are analysed. In particular, scenarios with natural flavour conservation are investigated, including the so-called type I and type II models as well as lepton-specific and inert models. Type III models are then discussed, where scalar flavour changing neutral currents are present at tree level, but are suppressed by either a specific ansatz for the Yukawa couplings or by the introduction of family symmetries leading to a natural suppression mechanism. We also consider the phenomenology of charged scalars in these models. Next we turn to the role of symmetries in the scalar sector. We discuss the six symmetry-constrained scalar potentials and their extension into the fermion sector. The vacuum structure of the scalar potential is analysed, including a study of the vacuum stability conditions on the potential and the renormalization-group improvement of these conditions is also presented. The stability of the tree level minimum of the scalar potential in connection with electric charge conservation and its behaviour under CP is analysed. The question of CP violation is addressed in detail, including the cases of explicit CP violation and spontaneous CP violation. We present a detailed study of weak basis invariants which are odd under CP. These invariants allow for the possibility of studying the CP properties of any two-Higgs-doublet model in an arbitrary Higgs basis. A careful study of spontaneous CP violation is presented, including an analysis of the conditions which have to be satisfied in order for a vacuum to violate CP. We present minimal models of CP violation where the vacuum phase is sufficient to generate a complex CKM matrix, which is at present a requirement for any realistic model of spontaneous CP violation.

Understanding multi-asset factor models: Factor exposure interpretation

Field lab: Business project