Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

Capital Requirements and Optimal Investment with Solvency Probability Constraints

Quantifying economic capital and optimally allocating it into portfolios of financial instruments are two key topics in the asset–liability management of an insurance company. In general, these problems are studied in the literature by minimizing standard risk measures such as the value at risk and the conditional VaR. Motivated by Solvency II regulations, we introduce a novel optimization problem to solve for the optimal required capital and the portfolio structure simultaneously, when the ruin probability is used as an insurance solvency constraint. Besides the generic optimal required capital and portfolio problem formulation, we propose a two-model hierarchy of optimization models, where both models admit the so-called second-order conic reformulation, in turn making them particularly well suited for numerics. The first model, albeit naively asserting the normality of the returns on assets and liabilities, under minor further simplifications admits a closed-form solution—a set of formulas, which may be used as simple decision-making guidelines in the analysis of more complex scenarios. A potentially more realistic second model aims to represent the ‘heavy-tailed’ nature of an insurer's liabilities more accurately, while also allowing arbitrary distributions of asset returns via a semi-parametric approach. Extensive numerical simulations illustrate the sensitivity and robustness of the proposed approach relative to the model's parameters. In addition, we explore the potential of insurance risk diversification and discuss if combining several liabilities into a single insurance portfolio may always be beneficial for the insurer. Finally, we propose an extension of the model with an expected return on capital constraint added

Modulation of SIRT1-foxo1 signaling axis by resveratrol: Implications in skeletal muscle aging and insulin resistance

© 2015 S. Karger AG, Basel. Aging individuals and diabetic patients often exhibit concomitant reductions of skeletal muscle mass/strength and insulin sensitivity, suggesting an intimate link between muscle aging and insulin resistance. Foxo1, a member of the FOXO transcription factor family, is an important player in insulin signaling due to its inhibitory role in glucose uptake and utilization in skeletal muscle. Phosphorylation of Foxo1 is thought to mitigate the transactivation of pyruvate dehydrogenase lipoamide kinase 4 (PDK4), which is a negative regulator of the glycolytic enzyme pyruvate dehydrogenase (PDH). In contrast, how aging would regulate acetylation/deacetylation machineries and glucose utilization in skeletal muscle through the Foxo1/PDH axis remains largely undetermined. Accumulating body of evidence have shown that resveratrol, a natural polyphenol in grapes and red wine, activates the longevity-related protein sirtuin 1 (SIRT1) and augments insulin sensitivity in addition to its well-documented effects on mitochondrial energetics. The present review summarizes the role of Foxo1/SIRT1 in insulin signaling in skeletal muscle and proposes the insight that activation of SIRT1 deacetylase activity to deacetylate and suppress the Foxo1-induced transactivation of PDK4 may represent an anti-hyperglycemic mechanism of resveratrol in aging skeletal muscle.Link_to_subscribed_fulltex

Suppression of both superconductivity and structural transition in hole-doped MoTe2_2 induced by Ta substitution

Type-II Weyl semimetal MoTe$_2$ exhibits a first-order structural transition at $T_s$ $\sim$250~K and superconducts at $T_c$ $\sim$0.1~K at ambient pressure. Both $T_s$ and $T_c$ can be manipulated by several tuning parameters, such as hydrostatic pressure and chemical substitution. It is often reported that suppressing $T_s$ enhances $T_c$, but our study shows a different behaviour when MoTe$_2$ is hole-doped by Ta. When $T_s$ is suppressed by Ta doping, $T_c$ is also suppressed. Our findings suggest that the suppression of $T_s$ does not necessarily enhance superconductivity in MoTe$_2$. By connecting with the findings of electron-doped MoTe$_2$, we argue that varying electron carrier concentration can effectively tune $T_c$. In addition, the Hall coefficient is enhanced around the doping region, where $T_s$ is completely suppressed, suggesting that the critical scattering around the structural transition may also play a role in suppressing $T_c$

Secretome Analysis of Skeletal Myogenesis Using SILAC and Shotgun Proteomics

Myogenesis, the formation of skeletal muscle, is a multistep event that commences with myoblast proliferation, followed by cell-cycle arrest, and finally the formation of multinucleated myotubes via fusion of mononucleated myoblasts. Each step is orchestrated by well-documented intracellular factors, such as cytoplasmic signalling molecules and nuclear transcription factors. Regardless, the key step in getting a more comprehensive understanding of the regulation of myogenesis is to explore the extracellular factors that are capable of eliciting the downstream intracellular factors. This could further provide valuable insight into the acute cellular response to extrinsic cues in maintaining normal muscle development. In this paper, we survey the intracellular factors that respond to extracellular cues that are responsible for the cascades of events during myogenesis: myoblast proliferation, cell-cycle arrest of myoblasts, and differentiation of myoblasts into myotubes. This focus on extracellular perspective of muscle development illustrates our mass spectrometry-based proteomic approaches to identify differentially expressed secreted factors during skeletal myogenesis

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Cohomology of bundles on homological Hopf manifold

We discuss the properties of complex manifolds having rational homology of $S^1 \times S^{2n-1}$ including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known vanishing properties of cohomology of bundles on such manifolds.As an application we consider degeneration of Hodge-deRham spectral sequence in this non Kahler setting.Comment: To appear in Proceedings of 2007 conference on Several complex variables and Complex Geometry. Xiamen. Chin