Separability and Fourier representations of density matrices

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d)$ is a basis for $d\times d$ matrices. If $N=d_{1}\times d_{2}\times...\times d_{b}$ and H^{[ N]}=\bigotimes H^{% [ d_{k}]}, we give a sufficient condition for separability of a density matrix $\rho$ relative to the $H^{[ d_{k}]}$ in terms of the $L_{1}$ norm of the spin coefficients of $\rho >.$ Since the spin representation depends on the form of the tensor product, the theory applies to both full and partial separability on a given space $H^{[ N]}$% . It follows from this result that for a prescribed form of separability, there is always a neighborhood of the normalized identity in which every density matrix is separable. We also show that for every prime $p$ and $n>1$ the generalized Werner density matrix $W^{[ p^{n}]}(s)$ is fully separable if and only if $s\leq (1+p^{n-1}) ^{-1}$

Wigner Functions and Separability for Finite Systems

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension p^n where p is a prime number. With this limitation it is possible to define a phase space and Wigner functions in close analogy to the continuous case. That is, we use a phase space that is a direct sum of n two-dimensional vector spaces each containing p^2 points. This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points. A useful aspect of this approach is that we can relate complete separability of density matrices and their Wigner functions in a natural way. We discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd. Special attention is required for two qubits (p=2) and our technique fails to establish the separability property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of the A matrices has been adde

Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior

Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus reverse-engineering attempts. This work is a contribution to the building of a set of stylized facts about the traders themselves. Using the client database of Swissquote Bank SA, the largest on-line Swiss broker, we find empirical relationships between turnover, account values and the number of assets in which a trader is invested. A theory based on simple mean-variance portfolio optimization that crucially includes variable transaction costs is able to reproduce faithfully the observed behaviors. We finally argue that our results bring into light the collective ability of a population to construct a mean-variance portfolio that takes into account the structure of transaction costsComment: 26 pages, 9 figures, Fig. 8 fixe

Revealing natural relationships among arbuscular mycorrhizal fungi: culture line BEG47 represents Diversispora epigaea, not Glomus versiforme

Background: Understanding the mechanisms underlying biological phenomena, such as evolutionarily conservative trait inheritance, is predicated on knowledge of the natural relationships among organisms. However, despite their enormous ecological significance, many of the ubiquitous soil inhabiting and plant symbiotic arbuscular mycorrhizal fungi (AMF, phylum Glomeromycota) are incorrectly classified. Methodology/Principal Findings: Here, we focused on a frequently used model AMF registered as culture BEG47. This fungus is a descendent of the ex-type culture-lineage of Glomus epigaeum, which in 1983 was synonymised with Glomus versiforme. It has since then been used as ‘G. versiforme BEG47’. We show by morphological comparisons, based on type material, collected 1860–61, of G. versiforme and on type material and living ex-type cultures of G. epigaeum, that these two AMF species cannot be conspecific, and by molecular phylogenetics that BEG47 is a member of the genus Diversispora. Conclusions: This study highlights that experimental works published during the last >25 years on an AMF named ‘G. versiforme’ or ‘BEG47’ refer to D. epigaea, a species that is actually evolutionarily separated by hundreds of millions of years from all members of the genera in the Glomerales and thus from most other commonly used AMF ‘laboratory strains’. Detailed redescriptions substantiate the renaming of G. epigaeum (BEG47) as D. epigaea, positioning it systematically in the order Diversisporales, thus enabling an evolutionary understanding of genetical, physiological, and ecological traits, relative to those of other AMF. Diversispora epigaea is widely cultured as a laboratory strain of AMF, whereas G. versiforme appears not to have been cultured nor found in the field since its original description

Acoustics and oceanographic observations collected during the QPE Experiment by Research Vessels OR1, OR2 and OR3 in the East China Sea in the Summer of 2009

This document describes data, sensors, and other useful information pertaining to the ONR sponsored QPE field program to quantify, predict and exploit uncertainty in observations and prediction of sound propagation. This experiment was a joint operation between Taiwanese and U.S. researchers to measure and assess uncertainty of predictions of acoustic transmission loss and ambient noise, and to observe the physical oceanography and geology that are necessary to improve their predictability. This work was performed over the continental shelf and slope northeast of Taiwan at two sites: one that was a relatively flat, homogeneous shelf region and a more complex geological site just shoreward of the shelfbreak that was influenced by the proximity of the Kuroshio Current. Environmental moorings and ADCP moorings were deployed and a shipboard SeaSoar vehicle was used to measure environmental spatial structure. In addition, multiple bottom moored receivers and a horizontal hydrophone array were deployed to sample transmission loss from a mobile source and ambient noise. The acoustic sensors, environmental sensors, shipboard resources, and experiment design, and their data, are presented and described in this technical report.Funding was provided by the Office of Naval Research under Contract No. N00014-08-1-076

Ernst Freund as Precursor of the Rational Study of Corporate Law

Gindis, David, Ernst Freund as Precursor of the Rational Study of Corporate Law (October 27, 2017). Journal of Institutional Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2905547, doi: https://dx.doi.org/10.2139/ssrn.2905547The rise of large business corporations in the late 19th century compelled many American observers to admit that the nature of the corporation had yet to be understood. Published in this context, Ernst Freund's little-known The Legal Nature of Corporations (1897) was an original attempt to come to terms with a new legal and economic reality. But it can also be described, to paraphrase Oliver Wendell Holmes, as the earliest example of the rational study of corporate law. The paper shows that Freund had the intuitions of an institutional economist, and engaged in what today would be called comparative institutional analysis. Remarkably, his argument that the corporate form secures property against insider defection and against outsiders anticipated recent work on entity shielding and capital lock-in, and can be read as an early contribution to what today would be called the theory of the firm.Peer reviewe

Biopolitics meets Terrapolitics: Political Ontologies and Governance in Settler-Colonial Australia

Crises persist in Australian Indigenous affairs because current policy approaches do not address the intersection of Indigenous and European political worlds. This paper responds to this challenge by providing a heuristic device for delineating Settler and Indigenous Australian political ontologies and considering their interaction. It first evokes Settler and Aboriginal ontologies as respectively biopolitical (focused through life) and terrapolitical (focused through land). These ideal types help to identify important differences that inform current governance challenges. The paper discusses the entwinement of these traditions as a story of biopolitical dominance wherein Aboriginal people are governed as an “included-exclusion” within the Australian political community. Despite the overall pattern of dominance, this same entwinement offers possibilities for exchange between biopolitics and terrapolitics, and hence for breaking the recurrent crises of Indigenous affairs

Mechanisms of congenital heart disease caused by NAA15 haploinsufficiency

Rationale: NAA15 is a component of the N-terminal (Nt) acetyltransferase complex, NatA. The mechanism by which NAA15 haploinsufficiency causes congenital heart disease (CHD) remains unknown. To better understand molecular processes by which NAA15 haploinsufficiency perturbs cardiac development, we introduced NAA15 variants into human induced pluripotent stem cells (iPSCs) and assessed the consequences of these mutations on RNA and protein expression. Objective: We aim to understand the role of NAA15 haploinsufficiency in cardiac development by investigating proteomic effects on NatA complex activity, and identifying proteins dependent upon a full amount of NAA15. Methods and Results: We introduced heterozygous LoF, compound heterozygous and missense residues (R276W) in iPS cells using CRISPR/Cas9. Haploinsufficient NAA15 iPS cells differentiate into cardiomyocytes, unlike NAA15-null iPS cells, presumably due to altered composition of NatA. Mass spectrometry (MS) analyses reveal ~80% of identified iPS cell NatA targeted proteins displayed partial or complete Nt-acetylation. Between null and haploinsufficient NAA15 cells Nt-acetylation levels of 32 and 9 NatA-specific targeted proteins were reduced, respectively. Similar acetylation loss in few proteins occurred in NAA15 R276W iPSCs. In addition, steady-state protein levels of 562 proteins were altered in both null and haploinsufficient NAA15 cells; eighteen were ribosomal-associated proteins. At least four proteins were encoded by genes known to cause autosomal dominant CHD. Conclusions: These studies define a set of human proteins that requires a full NAA15 complement for normal synthesis and development. A 50% reduction in the amount of NAA15 alters levels of at least 562 proteins and Nt-acetylation of only 9 proteins. One or more modulated proteins are likely responsible for NAA15-haploinsufficiency mediated CHD. Additionally, genetically engineered iPS cells provide a platform for evaluating the consequences of amino acid sequence variants of unknown significance on NAA15 function

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin