Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

Economics of neuraminidase inhibitor stock piling for pandemic influenza, Singapore.

We compared strategies for stock piling neuraminidase inhibitors to treat and prevent influenza in Singapore. Cost-benefit and cost-effectiveness analyses, with Monte Carlo simulations, were used to determine economic outcomes. A pandemic in a population of 4.2 million would result in an estimated 525-1,775 deaths, 10,700-38,600 hospitalization days, and economic costs of 0.7 dollars to 2.2 billion Singapore dollars. The treatment-only strategy had optimal economic benefits: stock piles of antiviral agents for 40% of the population would save an estimated 418 lives and 414 million dollars, at a cost of 52.6 million dollars per shelf-life cycle of the stock pile. Prophylaxis was economically beneficial in high-risk subpopulations, which account for 78% of deaths, and in pandemics in which the death rate was >0.6%. Prophylaxis for pandemics with a 5% case-fatality rate would save 50,000 lives and 81 billion dollars. These models can help policymakers weigh the options for pandemic planning

Independent ferroelectric contributions and rare-earth-induced polarization reversal in multiferroic TbMn2O5

Three independent contributions to the magnetically induced spontaneous polarization of multiferroic TbMn2O5 are uniquely separated by optical second harmonic generation and an analysis in terms of Landau theory. Two of them are related to the magnetic Mn3+/4+ order and are independent of applied fields of up to 7 T. The third contribution is related to the long-range antiferromagnetic Tb3+ order. It shows a drastic decrease upon the application of a magnetic field and mediates the change of sign of the spontaneous electric polarization in TbMn2O5. The close relationship between the rare-earth long-range order and the non-linear optical properties points to isotropic Tb-Tb exchange and oxygen spin polarization as mechanism for this rare-earth induced ferroelectricity.Comment: 8 pages, 5 figure

From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires

Electronic excitations above the ground state must overcome an energy gap in superconductors with spatially-homogeneous s-wave pairing. In contrast, inhomogeneous superconductors such as those with magnetic impurities or weak links, or heterojunctions containing normal metals or quantum dots, can host subgap electronic excitations that are generically known as Andreev bound states (ABSs). With the advent of topological superconductivity, a new kind of ABS with exotic qualities, known as Majorana bound state (MBS), has been discovered. We review the main properties of ABSs and MBSs, and the state-of-the-art techniques for their detection. We focus on hybrid superconductor-semiconductor nanowires, possibly coupled to quantum dots, as one of the most flexible and promising experimental platforms. We discuss how the combined effect of spin-orbit coupling and Zeeman field in these wires triggers the transition from ABSs into MBSs. We show theoretical progress beyond minimal models in understanding experiments, including the possibility of different types of robust zero modes that may emerge without a band-topological transition. We examine the role of spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.Comment: Review. 23 pages, 8 figures, 1 table. Shareable published version by Springer Nature at https://rdcu.be/b7DWT (free to read but not to download

DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise, so for typical sample sizes there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over DAGs, but not both. In this paper we leverage the fact that it is possible to estimate the "velocity" of gene expression with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time. Since our objective is to model uncertainty over discrete structures, we leverage Generative Flow Networks (GFlowNets) to estimate the posterior distribution over the combinatorial space of possible sparse dependencies. Our results indicate that our method learns posteriors that better encapsulate the distributions of cyclic structures compared to counterpart state-of-the-art Bayesian structure learning approaches

ZFIRE: The Evolution of the Stellar Mass Tully-Fisher Relation to Redshift 2.0 < Z < 2.5 with MOSFIRE

Using observations made with MOSFIRE on Keck I as part of the ZFIRE survey, we present the stellar mass Tully-Fisher relation at 2.0 < z < 2.5. The sample was drawn from a stellar mass limited, Ks-band selected catalog from ZFOURGE over the CANDELS area in the COSMOS field. We model the shear of the Halpha emission line to derive rotational velocities at 2.2X the scale radius of an exponential disk (V2.2). We correct for the blurring effect of a two-dimensional PSF and the fact that the MOSFIRE PSF is better approximated by a Moffat than a Gaussian, which is more typically assumed for natural seeing. We find for the Tully-Fisher relation at 2.0 < z < 2.5 that logV2.2 =(2.18 +/- 0.051)+(0.193 +/- 0.108)(logM/Msun - 10) and infer an evolution of the zeropoint of Delta M/Msun = -0.25 +/- 0.16 dex or Delta M/Msun = -0.39 +/- 0.21 dex compared to z = 0 when adopting a fixed slope of 0.29 or 1/4.5, respectively. We also derive the alternative kinematic estimator S0.5, with a best-fit relation logS0.5 =(2.06 +/- 0.032)+(0.211 +/- 0.086)(logM/Msun - 10), and infer an evolution of Delta M/Msun= -0.45 +/- 0.13 dex compared to z < 1.2 if we adopt a fixed slope. We investigate and review various systematics, ranging from PSF effects, projection effects, systematics related to stellar mass derivation, selection biases and slope. We find that discrepancies between the various literature values are reduced when taking these into account. Our observations correspond well with the gradual evolution predicted by semi-analytic models.Comment: 21 pages, 14 figures, 1 appendix. Accepted for publication by Apj, February 28, 201

Cooperative Carbon Dioxide Adsorption in Alcoholamine- and Alkoxyalkylamine-Functionalized Metal-Organic Frameworks.

A series of structurally diverse alcoholamine- and alkoxyalkylamine-functionalized variants of the metal-organic framework Mg2 (dobpdc) are shown to adsorb CO2 selectively via cooperative chain-forming mechanisms. Solid-state NMR spectra and optimized structures obtained from van der Waals-corrected density functional theory calculations indicate that the adsorption profiles can be attributed to the formation of carbamic acid or ammonium carbamate chains that are stabilized by hydrogen bonding interactions within the framework pores. These findings significantly expand the scope of chemical functionalities that can be utilized to design cooperative CO2 adsorbents, providing further means of optimizing these powerful materials for energy-efficient CO2 separations