Searches for new symmetries in pp collisions with the razor kinematic variables at √s = 7 TeV

The construction and LHC phenomenology of the razor variables M_R, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented.  The variables are used  in the analysis of the first proton-proton collisions dataset at CMS  (35 pb^-1) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results.  A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb^-1 of integrated luminosity from the second LHC run of 2011.  The selected events are analyzed in the 2D razor-space of M_R and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content.   The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with  gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively.

With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J^PC of this particle using the observed signal events in the H to ZZ^* to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW^* to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J^PC is discussed, with indications that this it could provide complementary information to the H to ZZ^* to 4 lepton final state, particularly for measuring CP-violation in these decays.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Discovery of non-zero neutrino mixing angle θ_13 using Daya Bay antineutrino detectors

The Daya Bay Reactor Antineutrino Experiment observed the disappearance of reactor $\bar{\nu}_e$ from six $2.9~GW_{th}$ reactor cores in Daya Bay, China. The Experiment consists of six functionally identical $\bar{\nu}_e$ detectors, which detect $\bar{\nu}_e$ by inverse beta decay using a total of about 120 metric tons of Gd-loaded liquid scintillator as the target volume. These $\bar{\nu}_e$ detectors were installed in three underground experimental halls, two near halls and one far hall, under the mountains near Daya Bay, with overburdens of 250 m.w.e, 265 m.w.e and 860 m.w.e. and flux-weighted baselines of 470 m, 576 m and 1648 m. A total of 90179 $\bar{\nu}_e$ candidates were observed in the six detectors over a period of 55 days, 57549 at the Daya Bay near site, 22169 at the Ling Ao near site and 10461 at the far site. By performing a rate-only analysis, the value of $sin^2 2\theta_{13}$ was determined to be $0.092 \pm 0.017$.

Variable-angle electron spectroscopic studies of various polyatomic molecular systems

The complementary techniques of low-energy, variable-angle electron-impact spectroscopy and ultraviolet variable-angle photoelectron spectroscopy have been used to study the electronic spectroscopy and structure of several series of molecules. Electron-impact studies were performed at incident beam energies between 25 eV and 100 eV and at scattering angles ranging from 0° to 90°. The energy-loss regions from 0 eV to greater than 15 eV were studied. Photoelectron spectroscopic studies were conducted using a HeI radiation source and spectra were measured at scattering angles from 45° to 90°. The molecules studied were chosen because of their spectroscopic, chemical, and structural interest. The operation of a new electron-impact spectrometer with multiple-mode target source capability is described. This spectrometer has been used to investigate the spin-forbidden transitions in a number of molecular systems.

The electron-impact spectroscopy of the six chloro-substituted ethylenes has been studied over the energy-loss region from 0-15 eV. Spin-forbidden excitations corresponding to the π → π*, N → T transition have been observed at excitation energies ranging from 4.13 eV in vinyl chloride to 3.54 eV in tetrachloroethylene. Symmetry-forbidden transitions of the type π → np have been oberved in trans-dichloroethyene and tetrachlor oethylene. In addition, transitions to many states lying above the first ionization potential were observed for the first time. Many of these bands have been assigned to Rydberg series converging to higher ionization potentials. The trends observed in the measured transition energies for the π → π*, N → T, and N → V as well as the π → 3s excitation are discussed and compared to those observed in the methyl- and fluoro- substituted ethylenes.

The electron energy-loss spectra of the group VIb transition metal hexacarbonyls have been studied in the 0 eV to 15 eV region. The differential cross sections were obtained for several features in the 3-7 eV energy-loss region. The symmetry-forbidden nature of the ¹A_1g → ¹A_1g, 2t_2g(π) → 3t_2g(π*) transition in these compounds was confirmed by the high-energy, low-angle behavior of their relative intensities. Several low lying transitions have been assigned to ligand field transitions on the basis of the energy and angular behavior of the differential cross sections for these transitions. No transitions which could clearly be assigned to singlet → triplet excitations involving metal orbitals were located. A number of states lying above the first ionization potential have been observed for the first time. A number of features in the 6-14 eV energy-loss region of the spectra of these compounds correspond quite well to those observed in free CO.

A number of exploratory studies have been performed. The π → π*, N → T, singlet → triplet excitation has been located in vinyl bromide at 4.05 eV. We have also observed this transition at approximately 3.8 eV in a cis-/trans- mixture of the 1,2-dibromoethylenes. The low-angle spectrum of iron pentacarbonyl was measured over the energy-loss region extending from 2-12 eV. A number of transitions of 8 eV or greater excitation energy were observed for the first time. Cyclopropane was also studied at both high and low angles but no clear evidence for any spin- forbidden transitions was found. The electron-impact spectrum of the methyl radical resulting from the pyrolysis of tetramethyl tin was obtained at 100 eV incident energy and at 0° scattering angle. Transitions observed at 5.70 eV and 8.30 eV agree well with the previous optical results. In addition, a number of bands were observed in the 8-14 eV region which are most likely due to Rydberg transitions converging to the higher ionization potentials of this molecule. This is the first reported electron-impact spectrum of a polyatomic free radical.

Variable-angle photoelectron spectroscopic studies were performed on a series of three-membered-ring heterocyclic compounds. These compounds are of great interest due to their highly unusual structure. Photoelectron angular distributions using HeI radiation have been measured for the first time for ethylene oxide and ethyleneimine. The measured anisotropy parameters, β, along with those measured for cyclopropane were used to confirm the orbital correlations and photoelectron band assignments. No high values of β similar to those expected for alkene π orbitals were observed for the Walsh or Forster-Coulson-Moffit type orbitals.

Magnetohydrodynamic turbulence

We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows.

1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves.

2) MHD turbulence is anisotropic with energy cascading more rapidly along k_⊥ than along k_∥, where k_⊥ and k_∥ refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_⊥ such that excited modes are confined inside a cone bounded by k_∥ ∝ k^γ_⊥ where γ less than 1. The opening angle of the cone, θ(k_⊥) ∝ k^-(1-γ)_⊥, defines the scale dependent anisotropy.

3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ² (k_⊥)≪1.

4) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/θ(k_⊥) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations.

6) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k by δ(t) correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance.

7) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up.

8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth by Goldreich and Sridhar (1995, 1997). Results from our simulations are also consistent with the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D power law spectra, E(k_⊥) ∝ k^-∝_⊥, determined from our simulations exhibit ∝ ≈ 3/2, whereas the GS model predicts ∝ = 5/3.

Structural and clumped-isotope constraints on the mechanisms of displacement along low-angle detachments

Despite years of research on low-angle detachments, much about them remains enigmatic. This thesis addresses some of the uncertainty regarding two particular detachments, the Mormon Peak detachment in Nevada and the Heart Mountain detachment in Wyoming and Montana.

Constraints on the geometry and kinematics of emplacement of the Mormon Peak detachment are provided by detailed geologic mapping of the Meadow Valley Mountains, along with an analysis of structural data within the allochthon in the Mormon Mountains. Identifiable structures well suited to constrain the kinematics of the detachment include a newly mapped, Sevier-age monoclinal flexure in the hanging wall of the detachment. This flexure, including the syncline at its base and the anticline at its top, can be readily matched to the base and top of the frontal Sevier thrust ramp, which is exposed in the footwall of the detachment to the east in the Mormon Mountains and Tule Springs Hills. The ~12 km of offset of these structural markers precludes the radial sliding hypothesis for emplacement of the allochthon.

The role of fluids in the slip along faults is a widely investigated topic, but the use of carbonate clumped-isotope thermometry to investigate these fluids is new. Faults rocks from within ~1 m of the Mormon Peak detachment, including veins, breccias, gouges, and host rocks, were analyzed for carbon, oxygen, and clumped-isotope measurements. The data indicate that much of the carbonate breccia and gouge material along the detachment is comminuted host rock, as expected. Measurements in vein material indicate that the fluid system is dominated by meteoric water, whose temperature indicates circulation to substantial depths (c. 4 km) in the upper crust near the fault zone.

Slip along the subhorizontal Heart Mountain detachment is particularly enigmatic, and many different mechanisms for failure have been proposed, predominantly involving catastrophic failure. Textural evidence of multiple slip events is abundant, and include multiple brecciation events and cross-cutting clastic dikes. Footwall deformation is observed in numerous exposures of the detachment. Stylolitic surfaces and alteration textures within and around “banded grains” previously interpreted to be an indicator of high-temperature fluidization along the fault suggest their formation instead via low-temperature dissolution and alteration processes. There is abundant textural evidence of the significant role of fluids along the detachment via pressure solution. The process of pressure solution creep may be responsible for enabling multiple slip events on the low-angle detachment, via a local rotation of the stress field.

Clumped-isotope thermometry of fault rocks associated with the Heart Mountain detachment indicates that despite its location on the flanks of a volcano that was active during slip, the majority of carbonate along the Heart Mountain detachment does not record significant heating above ambient temperatures (c. 40-70°C). Instead, cold meteoric fluids infiltrated the detachment breccia, and carbonate precipitated under ambient temperatures controlled by structural depth. Locally, fault gouge does preserve hot temperatures (>200°C), as is observed in both the Mormon Peak detachment and Heart Mountain detachment areas. Samples with very hot temperatures attributable to frictional shear heating are present but rare. They appear to be best preserved in hanging wall structures related to the detachment, rather than along the main detachment.

Evidence is presented for the prevalence of relatively cold, meteoric fluids along both shallow crustal detachments studied, and for protracted histories of slip along both detachments. Frictional heating is evident from both areas, but is a minor component of the preserved fault rock record. Pressure solution is evident, and might play a role in initiating slip on the Heart Mountain fault, and possibly other low-angle detachments.

Neural and computational representations of decision variables

These studies explore how, where, and when representations of variables critical to decision-making are represented in the brain. In order to produce a decision, humans must first determine the relevant stimuli, actions, and possible outcomes before applying an algorithm that will select an action from those available. When choosing amongst alternative stimuli, the framework of value-based decision-making proposes that values are assigned to the stimuli and that these values are then compared in an abstract “value space” in order to produce a decision. Despite much progress, in particular regarding the pinpointing of ventromedial prefrontal cortex (vmPFC) as a region that encodes the value, many basic questions remain. In Chapter 2, I show that distributed BOLD signaling in vmPFC represents the value of stimuli under consideration in a manner that is independent of the type of stimulus it is. Thus the open question of whether value is represented in abstraction, a key tenet of value-based decision-making, is confirmed. However, I also show that stimulus-dependent value representations are also present in the brain during decision-making and suggest a potential neural pathway for stimulus-to-value transformations that integrates these two results.

More broadly speaking, there is both neural and behavioral evidence that two distinct control systems are at work during action selection. These two systems compose the “goal-directed system”, which selects actions based on an internal model of the environment, and the “habitual” system, which generates responses based on antecedent stimuli only. Computational characterizations of these two systems imply that they have different informational requirements in terms of input stimuli, actions, and possible outcomes. Associative learning theory predicts that the habitual system should utilize stimulus and action information only, while goal-directed behavior requires that outcomes as well as stimuli and actions be processed. In Chapter 3, I test whether areas of the brain hypothesized to be involved in habitual versus goal-directed control represent the corresponding theorized variables.

The question of whether one or both of these neural systems drives Pavlovian conditioning is less well-studied. Chapter 4 describes an experiment in which subjects were scanned while engaged in a Pavlovian task with a simple non-trivial structure. After comparing a variety of model-based and model-free learning algorithms (thought to underpin goal-directed and habitual decision-making, respectively), it was found that subjects’ reaction times were better explained by a model-based system. In addition, neural signaling of precision, a variable based on a representation of a world model, was found in the amygdala. These data indicate that the influence of model-based representations of the environment can extend even to the most basic learning processes.

Knowledge of the state of hidden variables in an environment is required for optimal inference regarding the abstract decision structure of a given environment and therefore can be crucial to decision-making in a wide range of situations. Inferring the state of an abstract variable requires the generation and manipulation of an internal representation of beliefs over the values of the hidden variable. In Chapter 5, I describe behavioral and neural results regarding the learning strategies employed by human subjects in a hierarchical state-estimation task. In particular, a comprehensive model fit and comparison process pointed to the use of "belief thresholding". This implies that subjects tended to eliminate low-probability hypotheses regarding the state of the environment from their internal model and ceased to update the corresponding variables. Thus, in concert with incremental Bayesian learning, humans explicitly manipulate their internal model of the generative process during hierarchical inference consistent with a serial hypothesis testing strategy.

Minimum drag profiles in infinite cavity flows

The problem considered is that of minimizing the drag of a symmetric plate in infinite cavity flow under the constraints of fixed arclength and fixed chord. The flow is assumed to be steady, irrotational, and incompressible. The effects of gravity and viscosity are ignored.

Using complex variables, expressions for the drag, arclength, and chord, are derived in terms of two hodograph variables, Γ (the logarithm of the speed) and β (the flow angle), and two real parameters, a magnification factor and a parameter which determines how much of the plate is a free-streamline.

Two methods are employed for optimization:

(1) The parameter method. Γ and β are expanded in finite orthogonal series of N terms. Optimization is performed with respect to the N coefficients in these series and the magnification and free-streamline parameters. This method is carried out for the case N = 1 and minimum drag profiles and drag coefficients are found for all values of the ratio of arclength to chord.

(2) The variational method. A variational calculus method for minimizing integral functionals of a function and its finite Hilbert transform is introduced, This method is applied to functionals of quadratic form and a necessary condition for the existence of a minimum solution is derived. The variational method is applied to the minimum drag problem and a nonlinear integral equation is derived but not solved.