Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism

In a recent work, Markham and Sanders have proposed a framework to study quantum secret sharing (QSS) schemes using graph states. This framework unified three classes of QSS protocols, namely, sharing classical secrets over private and public channels, and sharing quantum secrets. However, most work on secret sharing based on graph states focused on threshold schemes. In this paper, we focus on general access structures. We show how to realize a large class of arbitrary access structures using the graph state formalism. We show an equivalence between $[[n,1]]$ binary quantum codes and graph state secret sharing schemes sharing one bit. We also establish a similar (but restricted) equivalence between a class of $[[n,1]]$ Calderbank-Shor-Steane (CSS) codes and graph state QSS schemes sharing one qubit. With these results we are able to construct a large class of quantum secret sharing schemes with arbitrary access structures.Comment: LaTeX, 6 page

A rapid and convergent synthesis of the integrastatin core

The tetracyclic core of the integrastatin natural products has been prepared in a convergent and rapidmanner. Our strategy relies upon a palladium(II)-catalyzed oxidative cyclization to form the central [3.3.1]-dioxabicycle of the natural product core. Overall, the core has been completed in only 4 linear steps from known compounds

Marketing and Data Science: Together the Future is Ours

The synergistic use of computer science and marketing science techniques offers the best avenue for knowledge development and improved applications. A broad area of complementarity between the typical focus in statistics and computer science and that in marketing offers great potential. The former fields tend to focus on pattern recognition, control and prediction. Many marketing analyses embrace these directions, but also contribute by modeling structure and exploring causal relationships. Marketing has successfully combined foci from management science with foci from psychology and economics. These fields complement each other because they enable a broad spectrum of scientific approaches. Combined, they provide both understanding and practical solutions to important and relevant managerial marketing problems, and marketing science is already very successful at obtaining unique insights from big data

On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system

In this paper, we consider a second order nonlinear ordinary differential equation of the form $\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$ are arbitrary parameters. By using the modified Prelle-Singer procedure, we identify five new integrable cases in this equation besides two known integrable cases, namely (i) $k_2=0, k_3=0$ and (ii) $k_1=0, k_2=0, k_5=0$. Among these five, four equations admit time dependent first integrals and the remaining one admits time independent first integral. From the time independent first integral, nonstandard Hamiltonian structure is deduced thereby proving the Liouville sense of integrability. In the case of time dependent integrals, we either explicitly integrate the system or transform to a time-independent case and deduce the underlying Hamiltonian structure. We also demonstrate that the above second order ordinary differential equation is intimately related to the two-dimensional Lotka-Volterra (LV) system. From the integrable parameters of above nonlinear equation and all the known integrable cases of the latter can be deduced thereby.Comment: Accepted for publication in J. Math. Phy