Algebraic Geometry of Matrix Product States

We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix product state or a limit of such states. For systems with few qubits, we give these equations explicitly, considering both periodic and open boundary conditions. Using the classical theory of trace varieties and trace algebras, we explain the relationship between MPS and hidden Markov models and exploit this relationship to derive useful parameterizations of MPS. We make four conjectures on the identifiability of MPS parameters

The generation and damping of propagating MHD kink waves in the solar atmosphere

The source of the non-thermal energy required for the heating of the upper solar atmosphere to temperatures in excess of a million degrees and the acceleration of the solar wind to hundreds of kilometers per second is still unclear. One such mechanism for providing the required energy flux is incompressible torsional Alfven and kink magnetohydrodynamic (MHD) waves, which are magnetically dominated waves supported by the Sun's pervasive and complex magnetic field. In particular, propagating MHD kink waves have recently been observed to be ubiquitous throughout the solar atmosphere, but, until now, critical details of the transport of the kink wave energy throughout the Sun's atmosphere were lacking. Here, the ubiquity of the waves is exploited for statistical studies in the highly dynamic solar chromosphere. This large-scale investigation allows for the determination of the chromospheric kink wave velocity power spectra, a missing link necessary for determining the energy transport between the photosphere and corona. Crucially, the power spectra contain evidence for horizontal photospheric motions being an important mechanism for kink wave generation in the quiescent Sun. In addition, a comparison with measured coronal power spectra is provided for the first time, revealing frequency-dependent transmission profiles, suggesting that there is enhanced damping of kink waves in the lower corona

Potential price variability in the US grain and livestock sector in the 1980s under alternative policy scenarios: an econometric approach

This study utilizes an annual structural econometric model of the U.S. grain and livestock sector to simulate market price instability resulting from potential fluctuations in domestic crop yields and demand for U.S. grain exports over 1981-90. The policy alternatives examined are a continuation of post-1977 grains policy and management strategy (PA I); elimination of grain policy programs (PA II); replacement of the existing farmer-owned reserve program (FOR) with an FOR equivalent subsidy to private commercial storage at any price (PA III); and continuation of post-1977 grains policy without authority to implement acreage reduction programs (PA IV);Results from estimation of the econometric model suggest that a l bushel increase in government carryover (FOR and CCC-owned stocks) displaces commercial carryover .242 and .259 bushels for wheat and feed grain, respectively. Impact multiplier analysis indicates that a l MMT (million metric ton) increase in government wheat and feed grain carryover increases current wheat and corn farm prices .16 and .02 per bushel, respectively. Such increases also increase current livestock price .001 and .004 (PL(,1979) = 2.62), respectively. FOR carryover for the 1977-80 period has been quite price elastic (estimated elasticities are 3.63 and 3.77 for wheat and feed grain). These estimates suggest that the reserve program as managed over 1977-80 has added to the elasticity of total demand for both wheat and feed grain, thus, significantly enhancing grain price stability;Mean grain and livestock prices generally follow each other fairly closely over the 1981-90 period for all policy alternatives. Wheat, corn, and livestock prices are 331, 38, and 17 percent more volatile, on average, over 1981-90 in the free market alternative (PA II) compared to the current policy alternative (PA I). These prices are 94, 29, and 13 percent more volatile when the FOR is replaced with a simple subsidy to all commercial storage at any price (PA III). Finally, results suggest that lack of acreage reduction authority (PA IV) requires FOR carryover to be 14 and 8 percent greater, on average, for wheat and feed grain (compared to PA I) to maintain market price volatility comparable to the current policy alternative

PROGRAMMED EFFECTS OF SURFACE WATER PRICE LEVELS ON U.S. AGRICULTURAL WATER USE AND PRODUCTION PATTERNS

Resource /Energy Economics and Policy,

Extracting Radial Velocities of A- and B-type Stars from Echelle Spectrograph Calibration Spectra

We present a technique to extract radial velocity measurements from echelle spectrograph observations of rapidly rotating stars ($V\sin{i} \gtrsim 50$ km s$^{-1}$). This type of measurement is difficult because the line widths of such stars are often comparable to the width of a single echelle order. To compensate for the scarcity of lines and Doppler information content, we have developed a process that forward-models the observations, fitting the radial velocity shift of the star for all echelle orders simultaneously with the echelle blaze function. We use our technique to extract radial velocity measurements from a sample of rapidly rotating A- and B-type stars used as calibrator stars observed by the California Planet Survey observations. We measure absolute radial velocities with a precision ranging from 0.5-2.0 km s$^{-1}$ per epoch for more than 100 A- and B-type stars. In our sample of 10 well-sampled stars with radial velocity scatter in excess of their measurement uncertainties, three of these are single-lined binaries with long observational baselines. From this subsample, we present detections of two previously unknown spectroscopic binaries and one known astrometric system. Our technique will be useful in measuring or placing upper limits on the masses of sub-stellar companions discovered by wide-field transit surveys, and conducting future spectroscopic binarity surveys and Galactic space-motion studies of massive and/or young, rapidly-rotating stars.Comment: Accepted to ApJ

The role of law in regimes of labour relations: A critique and corrective of comparative political economy

This thesis concerns the influential field of comparative political economy (CPE) and its leading approaches to labour relations ‘institutions’ and regimes in Europe. More specifically, this study offers both a critique and corrective of Varieties of Capitalism, Welfare State and Regulation approaches of CPE that have neglected the role of law, legal rules and legal systems in European labour relations. This thesis offers an alternative theoretical framework, a socio-legal political economy approach, developed principally out of existing CPE theory and contributions from legal studies. The thesis is organised according to a qualitative case study research design that sees two national examples of labour relations systems, Britain and Germany, compared using two areas of European Union law, acquired rights and posted workers, to develop this socio-legal political economy approach and draw conclusions. The four cases produce important findings in regards to specific aspects of labour relations concerning these two countries, collective bargaining and labour law. One broader theoretical argument stems from this comparative approach however. To theorise and compare evolving labour relations systems in Europe, the influence of law cannot be separated from emergence of neo-liberalism, its reforms, politics, practices and, crucially, its critically important legal characteristics. The result for CPE, is neither holistic and self-referential national models nor a singular neo-liberal ‘European’ model, but something much more complex and contested