Comment on "Weak Measurements with Orbital-Angular-Momentum Pointer states"

In a recent Letter (Phys. Rev. Lett. 109, 040401 (2012)), G. Puentes, N. Hermosa and J. P. Torres report a scheme for extracting higher-order weak values by using orbital-angular momentum states as pointer states. They claim that such weak values are inaccessible with a Gaussian pointer state only. In this Comment, we show that the Gaussian pointer state by itself can provide access to the higher-order weak value, if suitable pointer displacement is observed.Comment: Comment on: G. Puentes, N. Hermosa, J. P. Torres, Phys. Rev. Lett. 109, 040401 (2012) [arXiv:1204.3544

Pareto Boundary of the Rate Region for Single-Stream MIMO Interference Channels: Linear Transceiver Design

We consider a multiple-input multiple-output (MIMO) interference channel (IC), where a single data stream per user is transmitted and each receiver treats interference as noise. The paper focuses on the open problem of computing the outermost boundary (so-called Pareto boundary-PB) of the achievable rate region under linear transceiver design. The Pareto boundary consists of the strict PB and non-strict PB. For the two user case, we compute the non-strict PB and the two ending points of the strict PB exactly. For the strict PB, we formulate the problem to maximize one rate while the other rate is fixed such that a strict PB point is reached. To solve this non-convex optimization problem which results from the hard-coupled two transmit beamformers, we propose an alternating optimization algorithm. Furthermore, we extend the algorithm to the multi-user scenario and show convergence. Numerical simulations illustrate that the proposed algorithm computes a sequence of well-distributed operating points that serve as a reasonable and complete inner bound of the strict PB compared with existing methods.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Tans. Signal Process. June. 201

Dirac and Weyl Superconductors in Three Dimensions

We introduce the concept of 3D Dirac (Weyl) superconductors (SC), which have protected bulk four(two)-fold nodal points and surface Andreev arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry, e.g., the nodal phases of Cu$_x$Bi$_2$Se$_3$. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken. A Dirac node may split into a pair of Weyl nodes, only when time-reversal symmetry is broken.Comment: 5 pages and 2 figure

Exchange Rate Misalignment: A New Test of Long-Run PPP Based on Cross-Country Data (Subsequently published in "Applied Financial Economics", 16, 127-134, 2006. )

We formulate and implement a new empirical procedure to examine the validity of PPP in the long-run for 153 countries by using the familiar cross-country data set of Heston, Summers, and Aten (2002). Unlike the existing studies that rely on mean reversion of real exchange rates, we explicitly examine country-specificity in the deviations of the nominal exchange rate from PPP. We find, first, that out of a total of 153 countries, 132 countries have achieved PPP within twenty years, 1980-2000 and 105 countries have attained PPP over ten years, 1990-2000. Second, according to the results, our method can be accepted as a workable shortcut of the direct, fullinformation approach of Yotopoulos (1996) that tests for long-run PPP utilizing micro-ICP data. This becomes an important characteristic of this paper since comprehensive micro-ICP data are no longer easily available. As a by-product, of the empirical validation of our shortcut approach, our empirical results are in favor of the Ricardo-Balassa-Samuelson effect.

A consistent analytical formulation for volume-estimation of geometries enclosed by implicitly defined surfaces

We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all two-dimensional cases, and for elementary three three-dimensional cases by which the volume of general three-dimensional cases can be computed. Second, our method addresses the inconsistency issue due to mesh refinement. It is demonstrated by several two-dimensional and three-dimensional cases that this analytical formulation exhibits 2nd-order accuracy