Abstract Markowitz (1952, 1959) laid down the ground-breaking work on mean-variance analysis without gross exposure constraints. Under this framework, the theoretical optimal allocation vector can be different from the estimated one due to intrinsic difficulty of estimating a large covariance matrix and return vector. This can result in adverse performance in portfolio selected based on empirical data due to noise accumulation on estimation errors (Jagannathan and Ma, 2003; Fan, Fan and Lv, 2008). We address this problem by introducing the gross-exposure constrained mean-variance portfolio selection. We show that with gross-exposure constraint the theoretical optimal portfolios have similar performance as empirically selected ones based on estimated covariance matrices and there is no noise accumulation effect from estimation of covariance matrices. This gives theoretical justification to the empirical results

We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtain Heisenberg ⊕ Virasoro algebra with a central charge proportional to the gravitational Chern-Simons term of TMG. We also discuss that the flux of the chiral massive gravitons appears as the (Bondi) news through the null surface.

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The structural variations of multidomain proteins with flexible parts mediate many biological processes, and a structure ensemble can be determined by selecting a weighted combination of representative structures from a simulated structure pool, producing the best fit to experimental constraints such as interatomic distance. In this study, a hybrid structure-based and physics-based atomistic force field with an efficient sampling strategy is adopted to simulate a model di-domain protein against experimental paramagnetic relaxation enhancement (PRE) data that correspond to distance constraints. The molecular dynamics simulations produce a wide range of conformations depicted on a protein energy landscape. Subsequently, a conformational ensemble recovered with low-energy structures and the minimum-size restraint is identified in good agreement with experimental PRE rates, and the result is also supported by chemical shift perturbations and small-angle X-ray scattering data. It is illustrated that the regularizations of energy and ensemble-size prevent an arbitrary interpretation of protein conformations. Moreover, energy is found to serve as a critical control to refine the structure pool and prevent data overfitting, because the absence of energy regularization exposes ensemble construction to the noise from high-energy structures and causes a more ambiguous representation of protein conformations. Finally, we perform structure-ensemble optimizations with a topology-based structure pool, to enhance the understanding on the ensemble results from different sources of pool candidates.

Let X = (x_1,..,x_n) and Y = (y_1,...,y_m) be a pair of corresponding plaintext and ciphertext for a cryptosystem. We define an embedded surface of this cryptosystem as any polynomial equation: E(X,Y)=E(x_1,..,x_n,y_1,...,y_m)=0, which is satisfied by all such pairs. In this paper, we present a new attack on the multivariate public key cryptosystems from Diophantine equations developed by Gao and Heindl by using the embedded surfaces associated to this family of multivariate cryptosystems.