Sign Patterns of J-orthogonal Matrices

This thesis builds upon the results in “G-matrices, J-orthogonal matrices, and their sign patterns”, Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloˇzn ́ık. Some general results about the sign patterns of J-orthogonal matrices are proved, including about block diagonal matrices. It is shown that every full 4 × 4 sign pattern allows J -orthogonality and as a result that, for n ≤ 4, all n × n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. The 3 × 3 sign patterns of the J -orthogonal matrices which have zero entires are also characterized

Fluctuations in the Foreign Exchange Market: How Important are Monetary Policy Shocks?

We study the effects of U.S. monetary policy shocks on the bilateral exchange rate between the U.S. and each of the G7 countries. We also estimate deviations from uncovered interest rate parity and exchange rate pass-through conditional on these shocks. The analysis is based on a structural vector autoregression in which monetary policy shocks are identified through the conditional heteroscedasticity of the structural disturbances. Unlike earlier work in this area, our empirical methodology avoids making arbitrary assumptions about the relevant policy indicator or transmission mechanism in order to achieve identification. At the same time, it allows us to assess the implications of imposing invalid identifying restrictions. Our results indicate that the nominal exchange rate exhibits delayed overshooting in response to a monetary expansion, depreciating for roughly ten months before starting to appreciate. The shock also leads to large and persistent departures from uncovered interest rate parity, and to a prolonged period of incomplete pass-through. Variance-decomposition results indicate that monetary policy shocks account for a non-trivial proportion of exchange rate fluctuations.Conditions heteroscedasticity, delayed overshooting, exchange rate pass-through, identification, structural vector autoregression, uncovered interest rate parity

Monetary Policy Shocks: Testing Identification Conditions Under Time-Varying Conditional Volatility

We propose an empirical procedure, which exploits the conditional heteroscedasticity of fundamental disturbances, to test the targeting and orthogonality restrictions imposed in the recent VAR literature to identify monetary policy shocks. Based on U.S. monthly data for the post-1982 period, we reject the nonborrowed-reserve and interest-rate targeting procedures. In contrast, we present evidence supporting targeting procedures implying more than one policy variable. We also always reject the orthogonality conditions between policy shocks and macroeconomic variables. We show that using invalid restrictions often produces misleading policy measures and dynamic responses. These results have important implications for the measurement of policy shocks and their temporal effects as well as for the estimation of the monetary authority's reaction function.Conditional heteroscedasticity, monetary policy indicators, orthogonality conditions

Sparse regulatory networks

In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses $L_1$ penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS350 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fluctuating surface-current formulation of radiative heat transfer: theory and applications

We describe a novel fluctuating-surface current formulation of radiative heat transfer between bodies of arbitrary shape that exploits efficient and sophisticated techniques from the surface-integral-equation formulation of classical electromagnetic scattering. Unlike previous approaches to non-equilibrium fluctuations that involve scattering matrices---relating "incoming" and "outgoing" waves from each body---our approach is formulated in terms of "unknown" surface currents, laying at the surfaces of the bodies, that need not satisfy any wave equation. We show that our formulation can be applied as a spectral method to obtain fast-converging semi-analytical formulas in high-symmetry geometries using specialized spectral bases that conform to the surfaces of the bodies (e.g. Fourier series for planar bodies or spherical harmonics for spherical bodies), and can also be employed as a numerical method by exploiting the generality of surface meshes/grids to obtain results in more complicated geometries (e.g. interleaved bodies as well as bodies with sharp corners). In particular, our formalism allows direct application of the boundary-element method, a robust and powerful numerical implementation of the surface-integral formulation of classical electromagnetism, which we use to obtain results in new geometries, including the heat transfer between finite slabs, cylinders, and cones