Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure

Dynamic investment, debt structure and debt overhang

We study the impact of the optimal debt and priority structure on the intertwined corporate financing and investment decisions in a dynamic trade-off model, where the firm simultaneously uses bank and market debt for project financing. Private bank debt is renegotiable during financial distress, thus it avoids inefficient and costly bankruptcy losses should the renegotiation be successful. Our model shows: (i) Shareholders' bargaining power, renegotiation friction, growth potential, and bankruptcy costs limits bank debt capacity; (ii) The substitution effect between bank and market debt dominates in most cases; (iii) Bank debt issuance reduces the bankruptcy risk and speeds firm investment, which mitigates the debt overhand effect; (iv) Debt priority structure has a monotonic positive effect on firms' optimal capital structure, the net benefit of mixed debt financing, and firm valuation, the effect of which is much stronger for weaker shareholders, therefore, it would be optimal to place bank debt as senior for firm value maximization; (v) The benefit of mixed debt financing is significant (a firm valuation boost between 5%- 10% ) compared to either the bank debt exclusive or market debt exclusive debt structure

Dexmedetomidine post-treatment attenuates cardiac ischaemia/reperfusion injury by inhibiting apoptosis through HIF-1α signalling.

Hypoxia-inducible factor 1α (HIF-1α) plays a critical role in the apoptotic process during cardiac ischaemia/reperfusion (I/R) injury. This study aimed to investigate whether post-treatment with dexmedetomidine (DEX) could protect against I/R-induced cardiac apoptosis in vivo and in vitro via regulating HIF-1α signalling pathway. Rat myocardial I/R was induced by occluding the left anterior descending artery for 30 minutes followed by 6-hours reperfusion, and cardiomyocyte hypoxia/reoxygenation (H/R) was induced by oxygen-glucose deprivation for 6 hours followed by 3-hours reoxygenation. Dexmedetomidine administration at the beginning of reperfusion or reoxygenation attenuated I/R-induced myocardial injury or H/R-induced cell death, alleviated mitochondrial dysfunction, reduced the number of apoptotic cardiomyocytes, inhibited the activation of HIF-1α and modulated the expressions of apoptosis-related proteins including BCL-2, BAX, BNIP3, cleaved caspase-3 and cleaved PARP. Conversely, the HIF-1α prolyl hydroxylase-2 inhibitor IOX2 partly blocked DEX-mediated cardioprotection both in vivo and in vitro. Mechanistically, DEX down-regulated HIF-1α expression at the post-transcriptional level and inhibited the transcriptional activation of the target gene BNIP3. Post-treatment with DEX protects against cardiac I/R injury in vivo and H/R injury in vitro. These effects are, at least in part, mediated via the inhibition of cell apoptosis by targeting HIF-1α signalling

Bis{6,6′-dimeth­oxy-2,2′-[ethane-1,2-diyl­bis(imino­methyl­ene)]diphenolato(1.5−)-κ4 O,N,N′,O′}praeseodymium(III)

The title compound, [Pr(C18H22.5N2O4)2], is isotypic with its Er and Tb analogues. All interatomic distances, angles and the hydrogen bond geometry are very similar for the three structures.

Bis{6,6′-dimeth­oxy-2,2′-[ethane-1,2-diyl­bis(imino­methyl­ene)]diphenolato(1.5−)-κ4 O,N,N′,O′}terbium(III)

The title compound, [Tb(C18H22.5N2O4)2], is isotypic with its Pr and Tb analogues. All interatomic distances, angles and the hydrogen bond geometry are very similar for the three structures

Tetra­kis(μ-naphthalene-1-acetato-1:2κ2 O:O′)bis­(naphthalene-1-acetato)-1κ2 O,O′;2κ2 O,O′-bis­(1,10-phenanthroline)-1κ2 N,N′;2κ2 N,N′-europium(III)samarium(III)

In the title compound, [EuSm(C12H9O2)6(C12H8N2)2], the metal site is statistically occupied (50:50) by Eu and Sm atoms, forming a centrosymmetric complex. The metal site is nine-coordinate, in a distorted monocapped square-anti­prismatic coordination geometry. Mol­ecules are linked into three chains by C—H⋯π interactions and C—H⋯O hydrogen bonds. The combination of these chains generates a three-dimensional framework structure. One of the bridging naphthalene-1-ace­tate ligands was found to be disordered over two sites; the site occupancies for the naphthylmethyl group refined to 0.628 (14) and 0.372 (14)

Poly[(N,N-dimethyl­formamide-κO)tris­(μ-naphthalene-1-acetato)terbium(III)]

In title compound, [Tb(C12H9O2)3(C3H7NO)]n, the Tb atom is nine-coordinated by nine O atoms from three naphthalene-1-acetate and one N,N-dimethyl­formamide ligands. The Tb atoms are linked by three bridging naphthalene-1-acetate ligands into a chain parallel to the b axis. Further stabilization of the structure is accomplished by non-classical C—H⋯O hydrogen bonds and C—H⋯π interactions

Research on Rough Set Model Based on Golden Ratio

AbstractHow to make decision with pre-defined preference-ordered criteria also depends on the environment of the problem. Dominance rough set model is suitable for preference analysis and probabilistic rough set introduces probabilistic approaches to rough sets. In this paper, new dominance rough set rough set models are given by taking golden ratio into account. Also, we present steps to make decision using new dominance rough set models

1-Cyano-N-(2,4,5-trichloro­phen­yl)cyclo­propane-1-carboxamide

In the title compound, C11H7Cl3N3O, the dihedral angle between the benzene and cyclo­propane rings is 85.8 (2)°. In the crystal, mol­ecules are linked by C—H⋯O inter­actions, generating C(5) chains propagating in the a-axis direction