Local spin operators for fermion simulations

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on spins. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here we re-examine an auxiliary fermion construction which maps fermionic operators to local operators on spins. The local simulation is performed by relaxing the requirement that the number of spins should match the number of fermionic modes. Instead, auxiliary modes are introduced to enable non-consecutive fermionic couplings to be simulated with constant low-rank tensor products on spins. We connect the auxiliary fermion construction to other topological models and give examples of the construction

Entrepreneurial ecosystems: a dynamic lifecycle model

The concept of entrepreneurial ecosystems has been used as a framework to explain entrepreneurial activities within regions and industrial sectors. Despite the usefulness of this approach, the concept is under-theorized, especially with regard to the evolution of entrepreneurial ecosystems. The current literature is lacking a theoretical foundation that addresses the development and change of entrepreneurial ecosystems over time and does not consider the inherent dynamics of entrepreneurial ecosystems that lead to their birth, growth, maturity, decline, and re-emergence. Taking an industry lifecycle perspective, this paper addresses this research gap by elaborating a dynamic entrepreneurial ecosystem lifecycle model. We propose that an ecosystem transitions from an entrepreneurial ecosystem, with a focus on new firm creation, towards a business ecosystem, with a core focus on the internal commercialization of knowledge, i.e., intrapreneurial activities, and vice versa. Our dynamic model thus captures the oscillation that occurs among entrepreneurs and intrapreneurs through the different phases of an ecosystem’s lifecycle. Our dynamic lifecycle model may thus serve as a starting point for future empirical studies focusing on ecosystems and provide the basis for a further understanding of the interrelatedness between and co-existence of new and incumbent firms

Integrative Model-based clustering of microarray methylation and expression data

In many fields, researchers are interested in large and complex biological processes. Two important examples are gene expression and DNA methylation in genetics. One key problem is to identify aberrant patterns of these processes and discover biologically distinct groups. In this article we develop a model-based method for clustering such data. The basis of our method involves the construction of a likelihood for any given partition of the subjects. We introduce cluster specific latent indicators that, along with some standard assumptions, impose a specific mixture distribution on each cluster. Estimation is carried out using the EM algorithm. The methods extend naturally to multiple data types of a similar nature, which leads to an integrated analysis over multiple data platforms, resulting in higher discriminating power.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS533 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotics of Clebsch-Gordan Coefficients

Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example, six digit accuracy when the quantum numbers are in the hundreds.Comment: 30 pages, two figures. New Appendix added. Accepted for publication in the Journal of Mathematical Physic

On the Extraction of the Strong Coupling from Hadronic Tau Decay

The finite energy sum rule extraction of the strong coupling {\alpha}_s from hadronic {\tau} decay data provides one of its most precise experimental determinations. As precision improves, small non-perturbative effects become increasingly relevant to both the central value and error. Here we present a new framework for this extraction employing a physically motivated model to accommodate violations of quark-hadron duality and enforcing a consistent treatment of higher-dimension operator product expansion contributions. Using 1998 OPAL data for the non-strange vector and axial-vector spectral functions, we find the n_f=3 values for {\alpha}_s(m_{\tau}^2) of 0.307(19) for fixed-order perturbation theory and 0.322(26) for contour-improved perturbation theory, corresponding to n_f=5 values for {\alpha}_s(M_Z^2) of 0.1169(25) and 0.1187(32), respectively.Comment: 7 pages, contribution to Lattice 201

Adding ROS Scavengers to Cold K\u3csup\u3e+\u3c/sup\u3e Cardioplegia Reduces Superoxide Emission During 2 h Global Cold Cardiac Ischemia

We reported that the combination of reactive oxygen species (ROS) quenchers Mn(III) tetrakis (4-benzoic acid) porphyrin (MnTBAP), catalase, and glutathione (MCG) given before 2 hours cold ischemia better protected cardiac mitochondria against cold ischemia and warm reperfusion (IR)-induced damage than MnTBAP alone. Here, we hypothesize that high K+ cardioplegia (CP) plus MCG would provide added protection of mitochondrial bioenergetics and cardiac function against IR injury. Using fluorescence spectrophotometry, we monitored redox balance, ie reduced nicotinamide adenine dinucleotide and flavin adenine dinucleotide (NADH/FAD), superoxide (O2 •−), and mitochondrial Ca2+ (m[Ca2+]) in the left ventricular free wall. Guinea pig isolated hearts were perfused with either Krebs Ringer’s (KR) solution, CP, or CP + MCG, before and during 27°C perfusion followed immediately by 2 hours of global ischemia at 27°C. Drugs were washed out with KR at the onset of 2 hours 37°C reperfusion. After 120 minutes warm reperfusion, myocardial infarction was lowest in the CP + MCG group and highest in the KR group. Developed left ventricular pressure recovery was similar in CP and CP + MCG and was better than in the KR group. O2 •−, m[Ca2+], and NADH/FAD were significantly different between the treatment and KR groups. O2 •− was lower in CP + MCG than in the CP group. This study suggests that CP and ROS quenchers act in parallel to improve mitochondrial function and to provide protection against IR injury at 27°C

Convergence of the Many-Body Expansion of Interaction Potentials: From van der Waals to Covalent and Metallic Systems

The many-body expansion of the interaction potential between atoms and molecules is analyzed in detail for different types of interactions involving up to seven atoms. Elementary clusters of Ar, Na, Si, and, in particular, Au are studied, using first-principles wave-function- and density-functional-based methods to obtain the individual n-body contributions to the interaction energies. With increasing atom number the many-body expansion converges rapidly only for long-range weak interactions. Large oscillatory behavior is observed for other types of interactions. This is consistent with the fact that Au clusters up to a certain size prefer planar structures over the more compact three-dimensional Lennard-Jones-type structures. Several Au model potentials and semi-empirical PM6 theory are investigated for their ability to reproduce the quantum results. We further investigate small water clusters as prototypes of hydrogen-bonded systems. Here, the many-body expansion converges rapidly, reflecting the localized nature of the hydrogen bond and justifying the use of two-body potentials to describe water-water interactions. The question of whether electron correlation contributions can be successfully modeled by a many-body interaction potential is also addressed