Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

Scanning tunneling spectroscopy (STS) is a useful probe for studying the cuprates in the superconducting and pseudogap states. Here we present a theoretical study of the Z-map, defined as the ratio of the local density of states at positive and negative bias energies, which frequently is used to analyze STS data. We show how the evolution of the quasiparticle interference peaks in the Fourier transform Z-map can be understood by considering different types of impurity scatterers, as well as particle-hole asymmetry in the underlying bandstructure. We also explore the effects of density wave orders, and show that the Fourier transform Z-map may be used to both detect and distinguish between them.Comment: final version published in Phys. Rev.

Beta Power May Mediate the Effect of Gamma-TACS on Motor Performance

Transcranial alternating current stimulation (tACS) is becoming an important method in the field of motor rehabilitation because of its ability to non-invasively influence ongoing brain oscillations at arbitrary frequencies. However, substantial variations in its effect across individuals are reported, making tACS a currently unreliable treatment tool. One reason for this variability is the lack of knowledge about the exact way tACS entrains and interacts with ongoing brain oscillations. The present crossover stimulation study on 20 healthy subjects contributes to the understanding of cross-frequency effects of gamma (70 Hz) tACS over the contralateral motor cortex by providing empirical evidence which is consistent with a role of low- (12~-20 Hz) and high- (20-~30 Hz) beta power as a mediator of gamma-tACS on motor performance.Comment: 7 pages, 5 figures, in Proceedings of IEEE Engineering in Medicine and Biology Conference, July 2019 (IEEE license notice

Canadian Oil Sands Investments: FOCUS on a Controversial Energy Source

Rising energy demand and prices, particularly for oil, has led to a search for solutions to quell this increase. With the advent of the Oil Sands, we have stumbled upon an opportunity to increase Oil supplies and thus stabilize prices and satisfy demand. A large portion of the oil sands are located in Canada and this gives Canada an opportunity to improve its economy. Since the discovery, Canada has seen a vast influx in investment for the purpose of extracting these oil deposits. Using the University of Toronto's FOCUS model, which simulates the Canadian economy, this paper simulates and forecasts current and future trends in the Canadian economy that arise from this increase in investment. This paper breaks down the impacts on the various aspects of the Canadian economy and also analyzes many social issues that arise from the expansion of the oil sands, particularly the environmental issues. By doing so, one can analyze the current policies in place to deal with this expansion and revise them or create new policy which can prove more efficient in dealing with a potentially bubbling economy and the externalities that come from it.Oil Sands; Canada; Macroeconometrics; FOCUS model; Marcoeconomics; Econometrics; Energy; Oil;

Learning Mixtures of Gaussians in High Dimensions

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings

Cable Design for FAIR SIS 300

GSI, Darmstadt is preparing to build FAIR (Facility for Antiproton and Ion Research) which include SIS 300, a 300T - m fast-ramping heavy ion synchrotron. Dipoles for this ring will be 2.9 m long, producing 6 T over a 100 mm coil aperture and ramped at 1 T/s. The cable for these dipoles must have low losses and produce acceptable field distortions during the fast ramp. We plan to achieve this objective by using fine (~ 3 mum) filaments of NbTi in a wire with an interfilamentary matrix of CuMn to reduce proximity coupling and increase the transverse resistivity. The Rutherford cable have a thin stainless steel core and the wires will be coated with SnAg solder which has been oxidized, using a recipe similar to that developed at CERN, to increase the adjacent strand resistance Ra. Measurements of crossover strand resistance Re and Ra in cored cable with oxidized SnAg coating will be presented, together with data on critical current, persistent current magnetization and eddy current coupling in a wire with ultra fine filaments and a CuMn matrix in the interfilamentary region of the wire. These data will be used to predict losses and field distortion in the SIS 300 dipole and optimize the final design of cable for FAIR

Limits to substitution between ecosystem services and manufactured goods and implications for social discounting

This paper examines implications of limits to substitution for estimating substitutability between ecosystem services and manufactured goods and for social discounting. Based on a model that accounts for a subsistence requirement in the consumption of ecosystem services, we provide empirical evidence on substitution elasticities. We find an initial mean elasticity of substitution of two, which declines over time towards complementarity. We subsequently extend the theory of dual discounting by introducing a subsistence requirement. The relative price of ecosystem services is non-constant and grows without bound as the consumption of ecosystem services declines towards the subsistence level. An application suggests that the initial discount rate for ecosystem services is more than a percentage-point lower as compared to manufactured goods. This difference increases by a further half percentage-point over a 300-year time horizon. The results underscore the importance of considering limited substitutability in long-term public project appraisal