On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Electromagnetic signatures of lightning near the HF frequency band

The dissertation deals with remote narrowband measurements of the electromagnetic radiation emitted by lightning flashes. A lightning flash consists of a number of sub-processes. The return stroke, which transfers electrical charge from the thundercloud to to the ground, is electromagnetically an impulsive wideband process; that is, it emits radiation at most frequencies in the electromagnetic spectrum, but its duration is only some tens of microseconds. Before and after the return stroke, multiple sub-processes redistribute electrical charges within the thundercloud. These sub-processes can last for tens to hundreds of milliseconds, many orders of magnitude longer than the return stroke. Each sub-process causes radiation with specific time-domain characteristics, having maxima at different frequencies. Thus, if the radiation is measured at a single narrow frequency band, it is difficult to identify the sub-processes, and some sub-processes can be missed altogether. However, narrowband detectors are simple to design and miniaturize. In particular, near the High Frequency band (High Frequency, 3 MHz to 30 MHz), ordinary shortwave radios can, in principle, be used as detectors. This dissertation utilizes a prototype detector which is essentially a handheld AM radio receiver. Measurements were made in Scandinavia, and several independent data sources were used to identify lightning sub-processes, as well as the distance to each individual flash. It is shown that multiple sub-processes radiate strongly near the HF band. The return stroke usually radiates intensely, but it cannot be reliably identified from the time-domain signal alone. This means that a narrowband measurement is best used to characterize the energy of the radiation integrated over the whole flash, without attempting to identify individual processes. The dissertation analyzes the conditions under which this integrated energy can be used to estimate the distance to the flash. It is shown that flash-by-flash variations are large, but the integrated energy is very sensitive to changes in the distance, dropping as approximately the inverse cube root of the distance. Flashes can, in principle, be detected at distances of more than 100 km, but since the ground conductivity can vary, ranging accuracy drops dramatically at distances larger than 20 km. These limitations mean that individual flashes cannot be ranged accurately using a single narrowband detector, and the useful range is limited to 30 kilometers at the most. Nevertheless, simple statistical corrections are developed, which enable an accurate estimate of the distance to the closest edge of an active storm cell, as well as the approach speed. The results of the dissertation could therefore have practical applications in real-time short-range lightning detection and warning systems.

Search for Maximal Flavor Violating Scalars in Same-Charge Lepton Pairs in pp̅ Collisions at √s=1.96 TeV

Models of Maximal Flavor Violation (MxFV) in elementary particle physics may contain at least one new scalar SU$(2)$ doublet field $\Phi_{FV} = (\eta^0,\eta^+)$ that couples the first and third generation quarks ($q_1,q_3$) via a Lagrangian term $\mathcal{L}_{FV} = \xi_{13} \Phi_{FV} q_1 q_3$. These models have a distinctive signature of same-charge top-quark pairs and evade flavor-changing limits from meson mixing measurements. Data corresponding to 2 fb$^{-1}$ collected by the CDF II detector in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV are analyzed for evidence of the MxFV signature. For a neutral scalar $\eta^0$ with $m_{\eta^0} = 200$ GeV/$c^2$ and coupling $\xi_{13}=1$, $\sim$ 11 signal events are expected over a background of $2.1 \pm 1.8$ events. Three events are observed in the data, consistent with background expectations, and limits are set on the coupling $\xi_{13}$ for $m_{\eta^0} = 180-300$ GeV/$c^2$.

Exclusion of an Exotic Top Quark with -4/3 Electric Charge Using Soft Lepton Tagging

We present a measurement of the electric charge of the top quark using $\ppbar$ collisions corresponding to an integrated luminosity of 2.7~fb$^{-1}$ at the CDF II detector. We reconstruct $\ttbar$ events in the lepton+jets final state and use kinematic information to determine which $b$-jet is associated with the leptonically- or hadronically-decaying $t$-quark. Soft lepton taggers are used to determine the $b$-jet flavor. Along with the charge of the $W$ boson decay lepton, this information permits the reconstruction of the top quark's electric charge. Out of 45 reconstructed events with $2.4\pm0.8$ expected background events, 29 are reconstructed as $\ttbar$ with the standard model $+$2/3 charge, whereas 16 are reconstructed as $\ttbar$ with an exotic $-4/3$ charge. This is consistent with the standard model and excludes the exotic scenario at 95\% confidence level. This is the strongest exclusion of the exotic charge scenario and the first to use soft leptons for this purpose.

Search for New Bottomlike Quark Pair Decays QQ̅ →(tW∓)(t̅ W±) in Same-Charge Dilepton Events

We report the most restrictive direct limits on masses of fourth-generation down-type quarks b′, and quarklike composite fermions (B or T5/3), decaying promptly to tW∓. We search for a significant excess of events with two same-charge leptons (e, μ), several hadronic jets, and missing transverse energy. An analysis of data from pp̅ collisions with an integrated luminosity of 2.7  fb-1 collected with the CDF II detector at Fermilab yields no evidence for such a signal, setting mass limits mb′, mB>338  GeV/c2 and mT5/3>365  GeV/c2 at 95% confidence level.

Search for New Bottomlike Quark Pair Decays QQ̅ →(tW∓)(t̅ W±) in Same-Charge Dilepton Events

We report the most restrictive direct limits on masses of fourth-generation down-type quarks $b^{\prime}$, and quark-like composite fermions ($B$ or $T_{5/3}$), decaying promptly to $t W^{\mp}$. We search for a significant excess of events with two same-charge leptons ($e$, $\mu$), several hadronic jets, and missing transverse energy. An analysis of data from $p\overline{p}$ collisions with an integrated luminosity of 2.7 fb$^{-1}$ collected with the CDF II detector at Fermilab yields no evidence for such a signal, setting mass limits $m_{b^{\prime}}, m_{B} >$ 338 $\mathrm{GeV}/c^2$ and $m_{T_{5/3}} >$ 365 $\mathrm{GeV}/c^2$ at 95% confidence level.

Direct Measurement of the W Production Charge Asymmetry in pp̅ Collisions at √s=1.96 TeV

We present the first direct measurement of the $W$ production charge asymmetry as a function of the $W$ boson rapidity $\yW$ in $\ppbar$ collisions at $\sqrt{s} = 1.96$ $\TeV$. We use a sample of $\wenu$ events in data from 1 $\ifb$ of integrated luminosity collected using the CDF II detector. In the region $|\yW|