This note shows that we can recover any complex vector x 0 ∈ C n exactly from on the order of n quadratic equations of the form | a i , x 0 | 2 = b i , i = 1, . . . , m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. Further, we show that exact recovery holds for all input vectors simultaneously, and also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results.

In this paper we improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m × n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tractable ℓ 1 minimization even if a positive fraction of the measurements are arbitrarily corrupted, provided the number of nonzero entries in x is O(m/(log(n/m) + 1)). 2) In the very general sensing model introduced in [7] and assuming a positive fraction of corrupted measurements, exact recovery still holds if the signal now has O(m/(log 2 n)) nonzero entries. 3) Finally, we prove that one can recover an n × n low-rank matrix from m corrupted sampled entries by tractable optimization provided the rank is on the order of O(m/(n log 2 n)); again, this holds when there is a positive fraction of corrupted samples.

A qualitative informational similarity technique has been used to describe the informational orthogonality of projected two-dimensional (2-D) chromatographic separations of complex mixtures from their one-dimensional 1-D separations. The reversed-phase liquid chromatography (RPLC), supercritical fluid chromatography (SFC), gas-liquid chromatography (GLC), and micellar electrokinetic capillary chromatography (MECC) retention behavior of up to 46 solutes of varying molecular properties was studied by 2-D range-scaled retention time plots and information entropy calculations. One hundred five combinations of technique/stationary phase pairs were used to simulate the 2-D chromatographic analyses. The informational entropy of one and two dimensions, the mutual information, the synentropy or "cross information", and the informational similarity were calculated to describe the informational orthogonality. In addition, pattern descriptors were used to qualitatively describe the 2-D peak distribution. With the solutes tested, informational orthogonality, zero informational similarity, was observed with MECC-SDS/SFC-C1, MECC-SDS/SFC-Carbowax, MECC-TTAB/SFC-Carbowax, HPLC-C18/GLC-DB-5, HPLC-PBD/SFC-phenyl, SFC-Carbowax/GLC-DB5, and HPLC-phenyl/SFC-phenyl 2-D chromatographic systems. Conversely, with the solutes tested, informational nonorthogonal behavior described by range-scaled retention time plots to moderate to severe band overlap and data clustering was observed with 2-D chromatographic systems with high informational similarity and moderate to high degrees of synentropy. These results should prove useful for predicting complementary 2-D techniques as well as for choosing a second separation technique for confirmation of separation or peak purity.

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Abstract-We consider the problem of recovering a lowrank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been shown that this problem can be solved efficiently and effectively by a convex program named Principal Component Pursuit (PCP), provided that the fraction of corrupted entries and the rank of the matrix are both sufficiently small. In this paper, we extend that result to show that the same convex program, with a slightly improved weighting parameter, exactly recovers the low-rank matrix even if "almost all" of its entries are arbitrarily corrupted, provided the signs of the errors are random. We corroborate our result with simulations on randomly generated matrices and errors.

The effects of the Lambda n interaction on cross sections and Lambda polarization in the reaction ( gamma +d to K++ Lambda 0+n) are investigated in the spirit of the impulse approximation for three different potential models which have quite different scattering lengths and effective ranges. The authors find the interaction causes a significant enhancement of the cross section for the exclusive process d( gamma , K+ Lambda 0)n for selected kinematics near threshold, and not so significant an enhancement for the inclusive process d( gamma , K+) Lambda 0n. The produced Lambda tends to be depolarized and the polarization is sensitive to the potentials considered. The authors suggest that this reaction be used to extract information on the Lambda-neutron interaction by experiments being proposed for the new accelerators.

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Combined with educational information technology, advanced concepts of ubiquitous learning and mobile learning, the paper incorporates technologies of virtual reality, cloud computing, context awareness with blended learning mode in flipped classroom， which aims to meet the requirements of personalized teaching and learning by building a ubiquitous, smart and non-stop learning environment, which could truly achieve the student-centered teaching. Thus, in this paper, this VR-supported blended flipped classroom model was established and its features were analyzed, which could establish a three-dimensional virtual learning situation to simulate a user's physical presence in a virtual or imaginary environment, which is a brand new cognition experience. The model was applied in an empirical study of college English teaching through "English News" class. The results showed that this model achieved good teaching effects and had a guiding significance in advancing educational informatization both to improve students' overall cultural accomplishments and to meet the requirements of national, social and personal developments.Index Terms-Virtual reality, blended learning, flipped classroom, college English teaching.