A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation

We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.Comment: 5 pages, 1 figure; v2 has a simplified lattice, an extended analysis of errors, and some additional references; v3 published versio

A system for learning statistical motion patterns

Analysis of motion patterns is an effective approach for anomaly detection and behavior prediction. Current approaches for the analysis of motion patterns depend on known scenes, where objects move in predefined ways. It is highly desirable to automatically construct object motion patterns which reflect the knowledge of the scene. In this paper, we present a system for automatically learning motion patterns for anomaly detection and behavior prediction based on a proposed algorithm for robustly tracking multiple objects. In the tracking algorithm, foreground pixels are clustered using a fast accurate fuzzy k-means algorithm. Growing and prediction of the cluster centroids of foreground pixels ensure that each cluster centroid is associated with a moving object in the scene. In the algorithm for learning motion patterns, trajectories are clustered hierarchically using spatial and temporal information and then each motion pattern is represented with a chain of Gaussian distributions. Based on the learned statistical motion patterns, statistical methods are used to detect anomalies and predict behaviors. Our system is tested using image sequences acquired, respectively, from a crowded real traffic scene and a model traffic scene. Experimental results show the robustness of the tracking algorithm, the efficiency of the algorithm for learning motion patterns, and the encouraging performance of algorithms for anomaly detection and behavior prediction

A system for learning statistical motion patterns

Analysis of motion patterns is an effective approach for anomaly detection and behavior prediction. Current approaches for the analysis of motion patterns depend on known scenes, where objects move in predefined ways. It is highly desirable to automatically construct object motion patterns which reflect the knowledge of the scene. In this paper, we present a system for automatically learning motion patterns for anomaly detection and behavior prediction based on a proposed algorithm for robustly tracking multiple objects. In the tracking algorithm, foreground pixels are clustered using a fast accurate fuzzy k-means algorithm. Growing and prediction of the cluster centroids of foreground pixels ensure that each cluster centroid is associated with a moving object in the scene. In the algorithm for learning motion patterns, trajectories are clustered hierarchically using spatial and temporal information and then each motion pattern is represented with a chain of Gaussian distributions. Based on the learned statistical motion patterns, statistical methods are used to detect anomalies and predict behaviors. Our system is tested using image sequences acquired, respectively, from a crowded real traffic scene and a model traffic scene. Experimental results show the robustness of the tracking algorithm, the efficiency of the algorithm for learning motion patterns, and the encouraging performance of algorithms for anomaly detection and behavior prediction

Validating Sample Average Approximation Solutions with Negatively Dependent Batches

Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objective value and valuable information about the quality of the approximate solutions. Specifically, the lower bound can be estimated by solving multiple SAA problems (each obtained using a particular sampling method) and averaging the obtained objective values. State-of-the-art methods for lower-bound estimation generate batches of scenarios for the SAA problems independently. In this paper, we describe sampling methods that produce negatively dependent batches, thus reducing the variance of the sample-averaged lower bound estimator and increasing its usefulness in defining a confidence interval for the optimal objective value. We provide conditions under which the new sampling methods can reduce the variance of the lower bound estimator, and present computational results to verify that our scheme can reduce the variance significantly, by comparison with the traditional Latin hypercube approach

Stand-replacing wildfires increase nitrification for decades in southwestern ponderosa pine forests.

Stand-replacing wildfires are a novel disturbance within ponderosa pine (Pinus ponderosa) forests of the southwestern United States, and they can convert forests to grasslands or shrublands for decades. While most research shows that soil inorganic N pools and fluxes return to pre-fire levels within a few years, we wondered if vegetation conversion (ponderosa pine to bunchgrass) following stand-replacing fires might be accompanied by a long-term shift in N cycling processes. Using a 34-year stand-replacing wildfire chronosequence with paired, adjacent unburned patches, we examined the long-term dynamics of net and gross nitrogen (N) transformations. We hypothesized that N availability in burned patches would become more similar to those in unburned patches over time after fire as these areas become re-vegetated. Burned patches had higher net and gross nitrification rates than unburned patches (P < 0.01 for both), and nitrification accounted for a greater proportion of N mineralization in burned patches for both net (P < 0.01) and gross (P < 0.04) N transformation measurements. However, trends with time-after-fire were not observed for any other variables. Our findings contrast with previous work, which suggested that high nitrification rates are a short-term response to disturbance. Furthermore, high nitrification rates at our site were not simply correlated with the presence of herbaceous vegetation. Instead, we suggest that stand-replacing wildfire triggers a shift in N cycling that is maintained for at least three decades by various factors, including a shift from a woody to an herbaceous ecosystem and the presence of fire-deposited charcoal

Effect of uniaxial strain on the structural and magnetic phase transitions in BaFe2_2As2_2

We report neutron scattering experiments probing the influence of uniaxial strain on both the magnetic and structural order parameters in the parent iron pnictide compound, BaFe$_2$As$_2$. Our data show that modest strain fields along the in-plane orthorhombic b-axis can affect significant changes in phase behavior simultaneous to the removal of structural twinning effects. As a result, we demonstrate in BaFe$_2$As$_2$ samples detwinned via uniaxial strain that the in-plane C$_4$ symmetry is broken by \textit{both} the structural lattice distortion \textit{and} long-range spin ordering at temperatures far above the nominal (strain-free), phase transition temperatures. Surprising changes in the magnetic order parameter of this system under relatively small strain fields also suggest the inherent presence of magnetic domains fluctuating above the strain-free ordering temperature in this material.Comment: 4 pages, 3 figure

Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, λs. We use λs to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, λs, which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(λs) can be used to calculate elasticities

Universal magnetic and structural behaviors in the iron arsenides

Commonalities among the order parameters of the ubiquitous antiferromagnetism present in the parent compounds of the iron arsenide high temperature superconductors are explored. Additionally, comparison is made between the well established two-dimensional Heisenberg-Ising magnet, K$_2$NiF$_4$ and iron arsenide systems residing at a critical point whose structural and magnetic phase transitions coincide. In particular, analysis is presented regarding two distinct classes of phase transition behavior reflected in the development of antiferromagnetic and structural order in the three main classes of iron arsenide superconductors. Two distinct universality classes are mirrored in their magnetic phase transitions which empirically are determined by the proximity of the coupled structural and magnetic phase transitions in these materials.Comment: 6 pages, 4 figure

Changes in the soil organic carbon balance on China’s cropland during the last two decades of the 20th century

Agro-ecosystems play an important role in regulating global changes caused by greenhouse gas emissions. Restoration of soil organic carbon (SOC) in agricultural soils can not only improve soil quality but also influence climate change and agronomic productivity. With about half of its land area under agricultural use, China exhibits vast potential for carbon (C) sequestration that needs to be researched. Chinese cropland has experienced SOC change over the past century. The study of SOC dynamics under different bioclimatic conditions and cropping systems can help us to better understand this historical change, current status, the impacts of bioclimatic conditions on SOC and future trends. We used a simulation based on historical statistical data to analyze the C balance of Chinese croplands during the 1980s and 1990s, taking into account soil, climate and agricultural management. Nationwide, 77.6% of the national arable land is considered to be in good condition. Appropriate farm management practices should be adopted to improve the poor C balance of the remaining 22.4% of cropland to promote C sequestration