Interference is considered to be a major obstacle to wireless communication. Popular approaches, such as the zero-forcing receiver in MIMO (multiple-input and multiple-output) multiple-access channel (MAC) and zero-forcing (ZF) beamforming in MIMO broadcast channel (BC), eliminate the interference first and decode each codeword separately using a conventional single-user decoder. Recently, a transceiver architecture called integer-forcing (IF) has been proposed in the context of the MIMO Gaussian multiple-access channel to exploit integer-linear combinations of the codewords. Instead of treating other codewords as interference, the integer-forcing approach decodes linear combinations of the codewords from different users and solves for desired codewords. Integer-forcing can closely approach the performance of the optimal joint maximum likelihood decoder. An advanced version called successive integer-forcing can achieve the sum capacity of the MIMO MAC channel. Several extensions of integer-forcing have been developed in various scenarios, such as integer-forcing for the Gaussian MIMO broadcast channel, integer-forcing for Gaussian distributed source coding and integer-forcing interference alignment for the Gaussian interference channel. This dissertation demonstrates duality relationships for integer-forcing among three different channel models. We explore in detail two distinct duality types in this thesis: uplink-downlink duality and source-channel duality. Uplink-downlink duality is established for integer-forcing between the Gaussian MIMO multiple-access channel and its dual Gaussian MIMO broadcast channel. We show that under a total power constraint, integer-forcing can achieve the same sum rate in both cases. We further develop a dirty-paper integer-forcing scheme for the Gaussian MIMO BC and show an uplink-downlink duality with successive integer-forcing for the Gaussian MIMO MAC. The source-channel duality is established for integer-forcing between the Gaussian MIMO multiple-access channel and its dual Gaussian distributed source coding problem. We extend previous results for integer-forcing source coding to allow for successive cancellation. For integer-forcing without successive cancellation in both channel coding and source coding, we show the rates in two scenarios lie within a constant gap of one another. We further show that there exists a successive cancellation scheme such that both integer-forcing channel coding and integer-forcing source coding achieve the same rate tuple.

Next-generation wireless communication systems will need to contend with many active mobile devices, each of which will require a very high data rate. To cope with this growing demand, network deployments are becoming denser, leading to higher interference between active users. Conventional architectures aim to mitigate this interference through careful design of signaling and scheduling protocols. Unfortunately, these methods become less effective as the device density increases. One promising option is to enable cellular basestations (i.e., cell towers) to jointly process their received signals for decoding users’ data packets as well as to jointly encode their data packets to the users. This joint processing architecture is often enabled by a cloud radio access network that links the basestations to a central processing unit via dedicated connections. One of the main contributions of this thesis is a novel end-to-end communications architecture for cloud radio access networks as well as a detailed comparison to prior approaches, both via theoretical bounds and numerical simulations. Recent work has that the following high-level approach has numerous advantages: each basestation quantizes its observed signal and sends it to the central processing unit for decoding, which in turn generates signals for the basestations to transmit, and sends them quantized versions. This thesis follows an integer-forcing approach that uses the fact that, if codewords are drawn from a linear codebook, then their integer-linear combinations are themselves codewords. Overall, this architecture requires integer-forcing channel coding from the users to the central processing unit and back, which handles interference between the users’ codewords, as well as integer-forcing source coding from the basestations to the central processing unit and back, which handles correlations between the basestations’ analog signals. Prior work on integer-forcing has proposed and analyzed channel coding strategies as well as a source coding strategy for the basestations to the central processing unit, and this thesis proposes a source coding strategy for the other direction. Iterative algorithms are developed to optimize the parameters of the proposed architecture, which involve real-valued beamforming and equalization matrices and integer-valued coefficient matrices in a quadratic objective. Beyond the cloud radio setting, it is argued that the integer-forcing approach is a promising framework for interference alignment between multiple transmitter-receiver pairs. In this scenario, the goal is to align the interfering data streams so that, from the perspective of each receiver, there seems to be only a signal receiver. Integer-forcing interference alignment accomplishes this objective by having each receiver recover two linear combinations that can then be solved for the desired signal and the sum of the interference. Finally, this thesis investigates the impact of channel coherence on the integer-forcing strategy via numerical simulations.

Antarctic debris-covered glaciers are potential archives of long-term climate change. However, the geomorphic response of these systems to climate forcing is not well understood. To address this concern, I conducted a series of field-based and numerical modeling studies in the McMurdo Dry Valleys of Antarctica (MDV), with a focus on Mullins and Friedman glaciers. I used data and results from geophysical surveys, ice-core collection and analysis, geomorphic mapping, micro-meteorological stations, and numerical-process models to (1) determine the precise origin and distribution of englacial and supraglacial debris within these buried-ice systems, (2) quantify the fundamental processes and feedbacks that govern interactions among englacial and supraglacial debris, (3) establish a process-based model to quantify the inventory of cosmogenic nuclides within englacial and supraglacial debris, and (4) isolate the governing relationships between the evolution of englacial /supraglacial debris and regional climate forcing. Results from 93 field excavations, 21 ice cores, and 24 km of ground-penetrating radar data show that Mullins and Friedman glaciers contain vast areas of clean glacier ice interspersed with inclined layers of concentrated debris. The similarity in the pattern of englacial debris bands across both glaciers, along with model results that call for negligible basal entrainment, is best explained by episodic environmental change at valley headwalls. To constrain better the timing of debris-band formation, I developed a modeling framework that tracks the accumulation of cosmogenic 3He in englacial and supraglacial debris. Results imply that ice within Mullins Glacier increases in age non-linearly from 12 ka to ~220 ka in areas of active flow (up to >> 1.6 Ma in areas of slow-moving-to-stagnant ice) and that englacial debris bands originate with a periodicity of ~41 ka. Modeling studies suggest that debris bands originate in synchronicity with changes in obliquity-paced, total integrated summer insolation. The implication is that the englacial structure and surface morphology of some cold-based, debris-covered glaciers can preserve high-resolution climate archives that exceed the typical resolution of Antarctic terrestrial deposits and moraine records.

The Arctic climate has changed significantly in the last decades, experiencing a dramatic loss of sea ice and stronger than global warming. The Arctic surface temperature and the growth or melt of sea ice is determined by the local surface energy budget. In this context, clouds are of essential importance as they strongly interact with the radiative fluxes and modulate the surface energy budget depending on their properties, the surface types, and atmospheric thermodynamics. For the quantification of changes in the radiative energy budget (REB) associated with the presence or absence of clouds, the concept of cloud radiative forcing (CRF) is commonly used. This concept is defined as the differences between the REB in cloudy and cloud-free conditions, two atmospheric states which can not be observed at the same location and time. Consequently, either radiative transfer simulations or observations in both states have to be related, both of which complicate the derivation of CRF. A review of available studies and their approaches to derive the CRF reveals conceptual differences as well as deficiencies in the handling of radiative processes related to the surface albedo. These findings call into question the current state of CRF assessment in the Arctic based on the few available studies, but also their comparability. By combining atmospheric radiative transfer simulations with a snow albedo model, two processes that control the surface albedo during the transition from cloud-free to cloudy conditions and their role in the derivation of CRF are discussed. The broadband surface albedo of snow surfaces typically increases in the presence of clouds due to a spectral weighting of downward irradiance toward shorter wavelengths. For more absorbing surface types such as white ice and melt ponds, which are common in summer, there is a strong shift between the albedo of direct and diffuse illuminated surface, which diminishes the surface albedo depending on the cloud optical thickness and solar zenith angle. In this thesis, a hypothesis on the impact of those surface-albedo--cloud interactions on the annual cycle of shortwave CRF is discussed, but an application to inner Arctic conditions remains an open issue. An improved method to derive the shortwave CRF is proposed and an application to two airborne campaigns in the marginal sea ice zone northwest of Svalbard (Norway) illustrates the role of surface-albedo--cloud interactions in the Arctic in spring and early summer. For the longwave CRF, conceptual differences and the general interpretation of the different CRF estimates are discussed and illustrated for a case study. Radiative transfer simulations of a rarely observed annual cycle of thermodynamic profiles in the inner Arctic are used to study both longwave CRF approaches and the impact of thermodynamic profiles on the longwave CRF. Making use of airborne low-level flights in the MIZ and other available datasets, common seasonal radiative states on sea ice and case studies of warm air intrusions and cold air outbreaks are illustrated. The CRF is analyzed as a function of the observed cloud/surface regime, which is extended by radiative transfer simulations characterizing the conditions in this region and seasons.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20062号 / 工博第4250号 / 新制||工||1658(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 寶 馨, 教授 立川 康人, 准教授 佐山 敬洋 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

In der mittleren und oberen Atmosphäre spielen atmosphärische solare Gezeiten eine wichtige Rolle für die Dynamik und den Vertikaltransport von Energie und Impuls aus der Stratosphäre. Angeregt werden sie primär durch Absorption solarer Strahlung in der Troposphäre und Stratosphäre. Dabei entsprechen die Perioden der solaren Gezeiten den harmonischen Anteilen der täglichen Variation solarer Strahlung. Mittlerweile sind die täglichen, halbtägigen und dritteltägigen Gezeiten relativ gut erforscht, was bei der vierteltägigen Gezeit nicht der Fall ist. Die Informationen über diese Gezeit sind bislang rudimentär vor allem bzgl. einer globalen Klimatologie als auch der Details über möglichen Anregungsmechanismen und Wechselwirkungen. Dies ist darauf zurückzuführen, dass die Amplituden sehr klein sind und eine hohe zeitliche Auflösung für die Analyse benötigt wird. Die vierteltägige Gezeit wurde bislang von bodengebundenen Instrumenten und mit Fernerkundungsgsmethoden beobachtet, welche bislang lediglich einen räumlich und zeitlich begrenzten Überblick über die vierteltägige Gezeit boten. Da es nicht möglich ist die Beiträge der einzelnen Anregungen zu messen, muss sich numerischer Modelle als mächtiges Werkzeug bedient werden. Mit numerischen Modellen ist es möglich die verschiedenen Anregungsmechanismen zu separieren und ihre Beiträge für die vierteltägige Gezeit zu analysieren. Modellstudien lieferten bislang kein umfassendes Bild der QDT und berücksichtigten auch keine vierteltägige Schwerwellenanregungen. Diese Arbeit soll das Wissen zu diesem Thema erweitern, indem ein nichtlineares, mechanistisches, globales Zirkulationsmodell genutzt wird. Es wird eine umfassende numerische Studie durchgeführt, um die Wichtigkeit und das Zusammenspiel der drei vierteltägigen Anregungsmechanismen zu untersuchen, das sind die direkte solare Anregung, nichtlineare Wechselwirkung zwischen Gezeiten und Schwerewellen-Gezeiten-Wechselwirkungen. Erstmalig werden Anregungsterme, die über die Erwärmungsraten hinausgehen, selbst analysiert und quantifiziert und die Wechselwirkungen der vierteltägigen Gezeiten aus den unterschiedlichen Quellen untersucht. Darüber hinaus werden verschiedene Gezeitenmoden untersucht, um Interaktionen der vierteltätigen Gezeit aus den unterschiedlichen Anregungsmechanismen zu identifizieren. Darüber hinaus werden mit Hilfe der theoretischen Hough-Moden diejenigen Moden der vierteltägigen Gezeit abgeleitet, die in den Modellsimulationen maßgeblich für die meridionale Struktur verantwortlich sind. Diese aufwändige und umfassende Modellstudie analysiert die Anregungsmechanismen und deren Interaktion der vierteltägigen Gezeit. Die Arbeit hilft somit das Verständnis über die Wellenausbreitung der mittleren Atmosphäre auf ein neues Niveau zu heben.:1. Tides in the Middle Atmosphere - An Introduction 2. Quarterdiurnal Solar Tides 2.1. Forcing of Quarterdiurnal Tides 2.1.1. Overview of the different Forcing Mechanisms 2.1.2. Theoretical Consideration of the Nonlinear Forcing Mechanism 2.2. Observations and Model Study of the QDT 2.3. Summary and Outlook 3. The Middle and Upper Atmosphere Model (MUAM) 3.1. Introduction 3.2. Numerical Properties 3.3. Model Physics 3.4. Parameterizations 3.5. Background Climatology 4. Mathematical and Numerical Methods 4.1. Fast Fourier Transform 4.2. Harmonic Analysis 5. MUAM: Sensitivity Studies 5.1. Influence of Horizontal Resolution on the Background Climatology and QDT amplitudes 5.2. Influence of the Initial Conditions on the Background Climatology and QDT amplitudes 5.3. Influence of temporal resolution on the Background Climatology and QDT amplitudes 6. MUAM: Climatology of the Quarterdiurnal Tide 6.1. Amplitudes 6.2. Phases and Vertical Wavelengths 6.3. QDT reconstruction with Hough modes 7. MUAM: The Quarterdiurnal Tide Forcing Mechanisms 7.1. The Quarterdiurnal Forcing Terms 7.2. Model Experiments and Single Forcing Mechanisms 7.2.1. The Solar Forcing 7.2.2. The Gravity Wave Forcing 7.2.3. The Nonlinear Forcing 7.2.4. No Gravity Wave Forcing 7.2.5. No Nonlinear Forcing 7.3. Hough modes in Model experiments 7.3.1. SOL Hough modes 7.3.2. GW Hough modes 7.3.3. NLIN Hough modes 7.3.4. Hough modes: Seasonal cycle 7.4. Nonlinear Tidal Interactions 7.4.1. Model run without SDT/SDT interaction 7.4.2. Model run without DT/TDT interaction 7.4.3. Model run without tide-tide interaction 7.5. Solar Tidal Interactions 7.6. Interactions of Different Forcing Mechanisms 7.6.1. Interaction between Nonlinear and Solar Forcing 7.6.2. Interaction between Gravity wave and Solar Forcing 7.7. Influence of Enhanced Forcing Mechanisms 7.7.1. Influence of Enhanced Solar Forcing Mechanisms 7.7.2. Influence of Enhanced Gravity Wave Forcing Mechanisms 7.7.3. Influence of Enhanced Nonlinear Forcing Mechanisms 8. Summary and Conclusion 9. Outlook / In the middle and upper atmosphere atmospheric solar tides play an important role in the dynamics and vertical transport of energy and momentum from the stratosphere. They are primarily excited by absorption of solar radiation in the troposphere and stratosphere. The periods of the solar tides correspond to the harmonic components of the daily variation of solar radiation. Meanwhile, the diurnal, semidiurnal and terdiurnal tides have been relatively well studied, which is not the case with the quarterdiurnal tide. The knowledge about this tide is so far rudimentary, especially with regard to global climatology and details of possible excitation mechanisms and interactions. This is due to the fact that the amplitudes are very small and a high temporal resolution is required for the analysis. The quarterdiurnal tide has been observed by ground-based instruments and remote sensing methods, which until now have only provided a spatially and temporally limited overview of the quarterdiurnal tide. Since it is not possible to measure the contributions of the individual excitations, numerical models must be used as a powerful tool. With the numerical models it is possible to separate the different excitation mechanisms and to analyse their contributions for the quarterdiurnal tide. Model studies so far did not provide a comprehensive picture of QDT and did not consider QDT gravity wave excitation. This work is intended to extend the knowledge on this topic by using a nonlinear, mechanistic, global circulation model. A comprehensive numerical study will be carried out to investigate the importance and the interaction of the three quarterdiurnal excitation mechanisms, i.e. direct solar excitation, nonlinear tidal interactions and gravity wave tidal interactions. For the first time, excitation terms beyond the heating rates will be analyzed and quantified and the interactions of the quarterdiurnal tides from different sources will be investigated. Furthermore, different tidal modes will be investigated to identify quarterdiurnal tide interactions from the different excitation mechanisms. Furthermore, the theoretical Hough modes are used to derive those quarterdiurnal modes that are significantly responsible for the meridional structure in the model simulations. This elaborate and comprehensive model study analyses the excitation mechanisms and their interaction of the quarter-day tide. The work thus helps to raise the understanding of wave propagation in the middle atmosphere to a new level.:1. Tides in the Middle Atmosphere - An Introduction 2. Quarterdiurnal Solar Tides 2.1. Forcing of Quarterdiurnal Tides 2.1.1. Overview of the different Forcing Mechanisms 2.1.2. Theoretical Consideration of the Nonlinear Forcing Mechanism 2.2. Observations and Model Study of the QDT 2.3. Summary and Outlook 3. The Middle and Upper Atmosphere Model (MUAM) 3.1. Introduction 3.2. Numerical Properties 3.3. Model Physics 3.4. Parameterizations 3.5. Background Climatology 4. Mathematical and Numerical Methods 4.1. Fast Fourier Transform 4.2. Harmonic Analysis 5. MUAM: Sensitivity Studies 5.1. Influence of Horizontal Resolution on the Background Climatology and QDT amplitudes 5.2. Influence of the Initial Conditions on the Background Climatology and QDT amplitudes 5.3. Influence of temporal resolution on the Background Climatology and QDT amplitudes 6. MUAM: Climatology of the Quarterdiurnal Tide 6.1. Amplitudes 6.2. Phases and Vertical Wavelengths 6.3. QDT reconstruction with Hough modes 7. MUAM: The Quarterdiurnal Tide Forcing Mechanisms 7.1. The Quarterdiurnal Forcing Terms 7.2. Model Experiments and Single Forcing Mechanisms 7.2.1. The Solar Forcing 7.2.2. The Gravity Wave Forcing 7.2.3. The Nonlinear Forcing 7.2.4. No Gravity Wave Forcing 7.2.5. No Nonlinear Forcing 7.3. Hough modes in Model experiments 7.3.1. SOL Hough modes 7.3.2. GW Hough modes 7.3.3. NLIN Hough modes 7.3.4. Hough modes: Seasonal cycle 7.4. Nonlinear Tidal Interactions 7.4.1. Model run without SDT/SDT interaction 7.4.2. Model run without DT/TDT interaction 7.4.3. Model run without tide-tide interaction 7.5. Solar Tidal Interactions 7.6. Interactions of Different Forcing Mechanisms 7.6.1. Interaction between Nonlinear and Solar Forcing 7.6.2. Interaction between Gravity wave and Solar Forcing 7.7. Influence of Enhanced Forcing Mechanisms 7.7.1. Influence of Enhanced Solar Forcing Mechanisms 7.7.2. Influence of Enhanced Gravity Wave Forcing Mechanisms 7.7.3. Influence of Enhanced Nonlinear Forcing Mechanisms 8. Summary and Conclusion 9. Outlook

Aerosol–cloud interactions (ACIs) are considered to be the most uncertain driver of present-day radiative forcing due to human activities. The nonlinearity of cloud-state changes to aerosol perturbations make it challenging to attribute causality in observed relationships of aerosol radiative forcing. Using correlations to infer causality can be challenging when meteorological variability also drives both aerosol and cloud changes independently. Natural and anthropogenic aerosol perturbations from well-defined sources provide “opportunistic experiments” (also known as natural experiments) to investigate ACI in cases where causality may be more confidently inferred. These perturbations cover a wide range of locations and spatiotemporal scales, including point sources such as volcanic eruptions or industrial sources, plumes from biomass burning or forest fires, and tracks from individual ships or shipping corridors. We review the different experimental conditions and conduct a synthesis of the available satellite datasets and field campaigns to place these opportunistic experiments on a common footing, facilitating new insights and a clearer understanding of key uncertainties in aerosol radiative forcing. Cloud albedo perturbations are strongly sensitive to background meteorological conditions. Strong liquid water path increases due to aerosol perturbations are largely ruled out by averaging across experiments. Opportunistic experiments have significantly improved process-level understanding of ACI, but it remains unclear how reliably the relationships found can be scaled to the global level, thus demonstrating a need for deeper investigation in order to improve assessments of aerosol radiative forcing and climate change.

Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of matrices in S(G), sometimes diagonal entries corresponding to specific vertices of G must be zero for all matrices in MR(G). These vertices are known as nil vertices (see [6]). In this paper I discuss some basic results about nil vertices in general and nil vertices in cographs and prove that cographs with a nil vertex of a particular form contain two other nil vertices symmetric to the first. I discuss several open questions relating to these results and a counterexample. I prove that for all cographs G without an induced complete tripartite graph with independent sets all of size 3, the zero-forcing number Z(G), a graph theoretic parameter, is equal to M(G). In fact this result holds for a slightly larger class of cographs and in particular holds for all threshold graphs. Lastly, I prove that the maximum of the minimum ranks of all cographs on n vertices is the floor of 2n/3.

As soon as Bennett and Gill first demonstrated that, relative to a randomly chosen oracle, P is not equal to NP with probability 1, the random oracle hypothesis began piquing the interest of mathematicians and computer scientists. This was quickly disproven in several ways, most famously in 1992 with the result that IP equals PSPACE, in spite of the classes being shown unequal with probability 1. Here, we propose what could be considered strengthening of the random oracle hypothesis, using a stricter notion of what it means for a set to be 'large'. In particular, we suggest using largeness with respect to the Ramsey forcing notion. In this new context, we demonstrate that the set of oracles separating NP and coNP is 'not small', and obtain similar results for the separation of PSPACE from PH along with the separation of NP from BQP. In a related set of results, we demonstrate that these classes are all of the same descriptive complexity. Finally we demonstrate that this strengthening of the hypothesis turns it into a sufficient condition for unrelativized relationships, at least in the three cases considered here.

The focus of this thesis is the forcing mechanisms incorporated with salinity transport for the Lower St. Johns River. There are two primary analyses performed: a historical data analysis of primary forcing mechanisms to determine the importance of each individual influence, and a tidal hydrodynamics analysis for the Lower St. Johns River to determine the required tidal constituents for an accurate resynthesis. This thesis is a preliminary effort in understanding salinity transport for the Lower St. Johns River for engineering projects such as the dredging of navigation canals and freshwater withdrawal from the river. The analysis of the physical forcing mechanisms is performed by examining the impact of precipitation, tides, and wind advection on historical salinity measurements. Three 30-day periods were selected for the analysis, to correspond with representative peak, most-variable, and low-salinity periods for 1999. The analysis displays that wind advection is the dominant forcing mechanism for the movement of salinity over a 30 day duration; however all mechanisms have an impact at some level. The dominant forcing mechanism is also dependent on the period of record examined where tidal influence is vital for durations of hours to a day, while freshwater inflow has more significance over a longer period due to climatological variation. A two-dimensional finite difference numerical model is utilized to generate a one month tidal elevations and velocities simulations that incorporates geometry, nonlinear advection and quadratic bottom friction. Several combinations of tidal constituents are extracted from this modeled tidal signal to investigate which combination of tidal constituents produces an accurate tidal resynthesis for the Lower St. Johns River. The analysis displays the need for 39 total tidal harmonic constituents to accurately resynthesize the original tidal signal. Additionally, due to the nonlinear nature of shallow water, the influence of the overtides for upstream or downstream locations in the Lower St. Johns River is shown to be spatially variable for different frequencies depending on the geometry. The combination of the constituent analysis and the historical analysis provides the basis information needed for the development of an accurate salinity transport model for the Lower St. Johns River.