Power law decay for systems of randomly coupled differential equations

We consider large random matrices $X$ with centered, independent entries but possibly different variances. We compute the normalized trace of $f(X) g(X^*)$ for $f,g$ functions analytic on the spectrum of $X$. We use these results to compute the long time asymptotics for systems of coupled differential equations with random coefficients. We show that when the coupling is critical the norm squared of the solution decays like $t^{-1/2}$.Comment: 20 pages, Corrected a typo in Assumption (1) [after final publication] and made other irrelevant revision

The WACC Fallacy: The Real Effects of Using a Unique Discount Rate

We document investment distortions induced by the use of a single discount rate within firms. According to textbook capital budgeting, firms should value any project using a discount rate determined by the risk characteristics of the project. If they use a unique company-wide discount rate, they overinvest (resp. underinvest) in divisions with a market beta higher (resp. lower) than the firm's core industry beta. We directly test this consequence of the WACC fallacy and establish a robust and significant positive relationship between division-level investment and the spread between the division's market beta and the firm's core industry beta. Consistently with bounded rationality theories, this bias is stronger when the measured cost of taking the wrong discount rate is low, for instance, when the division is small. Finally, we measure the value loss due to the WACC fallacy in the context of acquisitions. Bidder abnormal returns are higher in diversifying mergers and acquisitions in which the bidder's beta exceeds that of the target. On average, the present value loss is about 0.7% of the bidder's market equity.Investment, Behavioral finance, Cost of capital

Singularity degree of structured random matrices

We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up, which we label the singularity degree

Characterization and Verification Environment for the RD53A Pixel Readout Chip in 65 nm CMOS

The RD53 collaboration is currently designing a large scale prototype pixel readout chip in 65 nm CMOS technology for the phase 2 upgrades at the HL-LHC. The RD53A chip will be available by the end of the year 2017 and will be extensively tested to confirm if the circuit and the architecture make a solid foundation for the final pixel readout chips for the experiments at the HL-LHC. A test and data acquisition system for the RD53A chip is currently under development to perform single-chip and multi-chip module measurements. In addition, the verification of the RD53A design is performed in a dedicated simulation environment. The concept and the implementation of the test and data acquisition system and the simulation environment, which are based on a modular data acquisition and system testing framework, are presented in this work

Randomly coupled differential equations with elliptic correlations

We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our previous work [14] that was restricted to the independent case. In particular, we analyze a recent model in the theory of neural networks [27] that specifically focused on the effect of the distributional asymmetry in the random connectivity matrix $X$. We rigorously prove and slightly correct the explicit formula from [28] on the time decay as a function of the asymmetry parameter. Our main tool is an asymptotically precise formula for the normalized trace of $f(X) g(X^*)$, in the large $N$ limit, where $f$ and $g$ are analytic functions.Comment: 46 pages, 4 figures. Paper has been reorganized. Examples have been adde

The WACC Fallacy: The Real Effects of Using a Unique Discount Rate

We document investment distortions induced by the use of a single discount rate within firms. According to textbook capital budgeting, firms should value any project using a discount rate determined by the risk characteristics of the project. If they use a unique company-wide discount rate, they overinvest (resp. underinvest) in divisions with a market beta higher (resp. lower) than the firm's core industry beta. We directly test this consequence of the WACC fallacy and establish a robust and significant positive relationship between division-level investment and the spread between the division's market beta and the firm's core industry beta. Consistently with bounded rationality theories, this bias is stronger when the measured cost of taking the wrong discount rate is low, for instance, when the division is small. Finally,we measure the value loss due to the WACC fallacy in the context of acquisitions. Bidder abnormal returns are higher in diversifying mergers and acquisitions in which the bidder's beta exceeds that of the target. On average, the present value loss is about 0.7% of the bidder's market equity

The WACC Fallacy: The Real Effects of Using a Unique Discount Rate

We document investment distortions induced by the use of a single discount rate within firms. According to textbook capital budgeting, firms should value any project using a discount rate determined by the risk characteristics of the project. If they use a unique company-wide discount rate, they overinvest (resp. underinvest) in divisions with a market beta higher (resp. lower) than the firm's core industry beta. We directly test this consequence of the WACC fallacy and establish a robust and significant positive relationship between division-level investment and the spread between the division's market beta and the firm's core industry beta. Consistently with bounded rationality theories, this bias is stronger when the measured cost of taking the wrong discount rate is low, for instance, when the division is small. Finally,we measure the value loss due to the WACC fallacy in the context of acquisitions. Bidder abnormal returns are higher in diversifying mergers and acquisitions in which the bidder's beta exceeds that of the target. On average, the present value loss is about 0.7% of the bidder's market equity

Geometrical torque on magnetic moments coupled to a correlated antiferromagnet

The geometrical spin torque mediates an indirect interaction of magnetic moments, which are weakly exchange coupled to a system of itinerant electrons. It originates from a finite spin-Berry curvature and leads to a non-Hamiltonian magnetic-moment dynamics. We demonstrate that there is an unprecedentedly strong geometrical spin torque in case of an electron system, where correlations cause antiferromagnetic long-range order. The key observation is that the anomalous torque is strongly boosted by low-energy magnon modes emerging in the two-electron spin-excitation spectrum due to spontaneous breaking of SU(2) spin-rotation symmetry. As long as single-electron excitations are gapped out, the effect is largely universal, i.e., essentially independent of the details of the electronic structure, but decisively dependent on the lattice dimension and spatial and spin anisotropies. Analogous to the reasoning that leads to the Mermin-Wagner theorem, there is a lower critical dimension at and below which the spin-Berry curvature diverges.Comment: 5 pages, 3 figures, suppl. materia

Development and Application of an Atomic Absorption Spectrometry-Based Method to Quantify Magnesium in Leaves of Dioscorea polystachya

The Chinese yam (Dioscorea polystachya, DP) is known for the nutritional value of its tuber. Nevertheless, DP also has promising pharmacological properties. Compared with the tuber, the leaves of DP are still very little studied. However, it may be possible to draw conclusions about the plant quality based on the coloration of the leaves. Magnesium, as a component of chlorophyll, seems to play a role. Therefore, the aim of this research work was to develop an atomic absorption spectrometry-based method for the analysis of magnesium (285.2125 nm) in leaf extracts of DP following the graphite furnace sub-technique. The optimization of the pyrolysis and atomization temperatures resulted in 1500 °C and 1800 °C, respectively. The general presence of flavonoids in the extracts was detected and could explain the high pyrolysis temperature due to the potential complexation of magnesium. The elaborated method had linearity in a range of 1–10 µg L−1 (R2 = 0.9975). The limits of detection and quantification amounted to 0.23 µg L−1 and 2.00 µg L−1, respectively. The characteristic mass was 0.027 pg, and the recovery was 96.7–102.0%. Finally, the method was applied to extracts prepared from differently colored leaves of DP. Similar magnesium contents were obtained for extracts made of dried and fresh leaves. It is often assumed that the yellowing of the leaves is associated with reduced magnesium content. However, the results indicated that yellow leaves are not due to lower magnesium levels. This stimulates the future analysis of DP leaves considering other essential minerals such as molybdenum or manganese