Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D ±J\pm J Random-Bond Ising Model

The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$ are studied. We are able to consider large samples of up to $320^2$ spins by using sophisticated matching algorithms. We study $L \times L$ systems, but we also consider $L \times M$ samples, for different aspect ratios $R = L / M$. We find that the scaling behavior of the ground-state energy and its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le 1 - p_c$) are characterized by simple scaling functions. In particular, the fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass region the average domain-wall energy converges to a finite nonzero value as the sample size becomes infinite, holding $R$ fixed. Here, large finite-size effects are visible, which can be explained for all $p$ by a single exponent $\omega\approx 2/3$, provided higher-order corrections to scaling are included. Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the distribution of the domain-wall energies converges to a Gaussian for $R \to 0$, although the domain walls of neighboring subsystems of size $L \times L$ are not independent.Comment: 11 pages with 15 figures, extensively revise

Reduction of Two-Dimensional Dilute Ising Spin Glasses

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see http://www.physics.emory.edu/faculty/boettcher

Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

Quantum Zeno stabilization in weak continuous measurement of two qubits

We have studied quantum coherent oscillations of two qubits under continuous measurement by a symmetrically coupled mesoscopic detector. The analysis is based on a Bayesian formalism that is applicable to individual quantum systems. Measurement continuously collapses the two-qubit system to one of the sub-spaces of the Bell basis. For a detector with linear response this corresponds to measurement of the total spin of the qubits. In the other extreme of purely quadratic response the operator \sigma_y^1 \sigma_y^2 + \sigma_z^1 \sigma_z^2 is measured. In both cases, collapse naturally leads to spontaneous entanglement which can be identified by measurement of the power spectrum and/or the average current of the detector. Asymmetry between the two qubits results in evolution between the different measurement subspaces. However, when the qubits are even weakly coupled to the detector, a kind of quantum Zeno effect cancels the gradual evolution and replaces it with rare, abrupt switching events. We obtain the asymptotic switching rates for these events and confirm them with numerical simulations. We show how such switching affects the observable power spectrum on different time scales.Comment: 18 pages, 8 eps figures, reference adde

Defining Meyer's loop-temporal lobe resections, visual field deficits and diffusion tensor tractography

Anterior temporal lobe resection is often complicated by superior quadrantic visual field deficits (VFDs). In some cases this can be severe enough to prohibit driving, even if a patient is free of seizures. These deficits are caused by damage to Meyer's loop of the optic radiation, which shows considerable heterogeneity in its anterior extent. This structure cannot be distinguished using clinical magnetic resonance imaging sequences. Diffusion tensor tractography is an advanced magnetic resonance imaging technique that enables the parcellation of white matter. Using seed voxels antero-lateral to the lateral geniculate nucleus, we applied this technique to 20 control subjects, and 21 postoperative patients. All patients had visual fields assessed with Goldmann perimetry at least three months after surgery. We measured the distance from the tip of Meyer's loop to the temporal pole and horn in all subjects. In addition, we measured the size of temporal lobe resection using postoperative T1-weighted images, and quantified VFDs. Nine patients suffered VFDs ranging from 22% to 87% of the contralateral superior quadrant. In patients, the range of distance from the tip of Meyer's loop to the temporal pole was 24–43 mm (mean 34 mm), and the range of distance from the tip of Meyer's loop to the temporal horn was –15 to +9 mm (mean 0 mm). In controls the range of distance from the tip of Meyer's loop to the temporal pole was 24–47 mm (mean 35 mm), and the range of distance from the tip of Meyer's loop to the temporal horn was –11 to +9 mm (mean 0 mm). Both quantitative and qualitative results were in accord with recent dissections of cadaveric brains, and analysis of postoperative VFDs and resection volumes. By applying a linear regression analysis we showed that both distance from the tip of Meyer's loop to the temporal pole and the size of resection were significant predictors of the postoperative VFDs. We conclude that there is considerable variation in the anterior extent of Meyer's loop. In view of this, diffusion tensor tractography of the optic radiation is a potentially useful method to assess an individual patient's risk of postoperative VFDs following anterior temporal lobe resection

Kerr-Schild Approach to the Boosted Kerr Solution

Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and the Kerr theorem we analyze the boosted Kerr geometries and give the exact and explicit expressions for the metrics, the principal null congruences, the coordinate systems and the location of the singularities for arbitrary value and orientation of the boost with respect to the angular momentum. In the limiting, ultrarelativistic case we obtain light-like solutions possessing diverging and twisting principal null congruences and having, contrary to the known pp-wave limiting solutions, a non-zero value of the total angular momentum. The implications of the above results in various related fields are discussed.Comment: 16 pages, LaTe

Climate Change during and after the Roman Empire: Reconstructing the Past from Scientific and Historical Evidence

Growing scientific evidence from modern climate science is loaded with implications for the environmental history of the Roman Empire and its successor societies. The written and archaeological evidence, although richer than commonly realized, is unevenly distributed over time and space. A first synthesis of what the written records and multiple natural archives (multi-proxy data) indicate about climate change and variability across western Eurasia from c. 100 b.c. to 800 a.d. confirms that the Roman Empire rose during a period of stable and favorable climatic conditions, which deteriorated during the Empire's third-century crisis. A second, briefer period of favorable conditions coincided with the Empire's recovery in the fourth century; regional differences in climate conditions parallel the diverging fates of the eastern and western Empires in subsequent centuries. Climate conditions beyond the Empire's boundaries also played an important role by affecting food production in the Nile valley, and by encouraging two major migrations and invasions of pastoral peoples from Central Asia.Earth and Planetary SciencesHistor

Placing the east-west North American aridity gradient in a multi-century context

Instrumental records indicate a century-long trend towards drying over western North America and wetting over eastern North America. A continuation of these trends into the future would have significant hydroclimatic and socioeconomic consequences in both the semi-arid Southwest and humid East. Using tree-ring reconstructions and hydrologic simulations of summer soil moisture, we evaluate and contextualize the modern summer aridity gradient within its natural range of variability established over the past 600 years and evaluate the effects of observed and anthropogenic precipitation, temperature, and humidity trends. The 2001–2020 positive (wet east-dry west) aridity gradient was larger than any 20 year period since 1400 CE, preceded by the most negative (wet west-dry east) aridity gradient during 1976–1995, leading to a strong multi-decade reversal in aridity gradient anomalies that was rivaled only by a similar event in the late-16th century. The 2001–2020 aridity gradient was dominated by long-term summer precipitation increases in the Midwest and Northeast, with smaller contributions from more warming in the West than the East and spring precipitation decreases in the Southwest. Multi-model mean climate simulations from Coupled Model Intercomparison Project 6 experiments suggest anthropogenic climate trends should not have strongly affected the aridity gradient thus far. However, there is high uncertainty due to inter-model disagreement on anthropogenic precipitation trends. The recent strengthening of the observed aridity gradient, its increasing dependence on precipitation variability, and disagreement in modeled anthropogenic precipitation trends reveal significant uncertainties in how water resource availability will change across North America in the coming decades

First Steps towards Underdominant Genetic Transformation of Insect Populations

The idea of introducing genetic modifications into wild populations of insects to stop them from spreading diseases is more than 40 years old. Synthetic disease refractory genes have been successfully generated for mosquito vectors of dengue fever and human malaria. Equally important is the development of population transformation systems to drive and maintain disease refractory genes at high frequency in populations. We demonstrate an underdominant population transformation system in Drosophila melanogaster that has the property of being both spatially self-limiting and reversible to the original genetic state. Both population transformation and its reversal can be largely achieved within as few as 5 generations. The described genetic construct {Ud} is composed of two genes; (1) a UAS-RpL14.dsRNA targeting RNAi to a haploinsufficient gene RpL14 and (2) an RNAi insensitive RpL14 rescue. In this proof-of-principle system the UAS-RpL14.dsRNA knock-down gene is placed under the control of an Actin5c-GAL4 driver located on a different chromosome to the {Ud} insert. This configuration would not be effective in wild populations without incorporating the Actin5c-GAL4 driver as part of the {Ud} construct (or replacing the UAS promoter with an appropriate direct promoter). It is however anticipated that the approach that underlies this underdominant system could potentially be applied to a number of species. Figure