Optimality of Graphlet Screening in High Dimensional Variable Selection

Consider a linear regression model where the design matrix X has n rows and p columns. We assume (a) p is much large than n, (b) the coefficient vector beta is sparse in the sense that only a small fraction of its coordinates is nonzero, and (c) the Gram matrix G = X'X is sparse in the sense that each row has relatively few large coordinates (diagonals of G are normalized to 1). The sparsity in G naturally induces the sparsity of the so-called graph of strong dependence (GOSD). We find an interesting interplay between the signal sparsity and the graph sparsity, which ensures that in a broad context, the set of true signals decompose into many different small-size components of GOSD, where different components are disconnected. We propose Graphlet Screening (GS) as a new approach to variable selection, which is a two-stage Screen and Clean method. The key methodological innovation of GS is to use GOSD to guide both the screening and cleaning. Compared to m-variate brute-forth screening that has a computational cost of p^m, the GS only has a computational cost of p (up to some multi-log(p) factors) in screening. We measure the performance of any variable selection procedure by the minimax Hamming distance. We show that in a very broad class of situations, GS achieves the optimal rate of convergence in terms of the Hamming distance. Somewhat surprisingly, the well-known procedures subset selection and the lasso are rate non-optimal, even in very simple settings and even when their tuning parameters are ideally set

The roles of fungus in CNS autoimmune and neurodegeneration disorders

Fungal infection or proliferation in our body is capable of initiation of strong inflammation and immune responses that result in different consequences, including infection-trigged organ injury and inflammation-related remote organ dysfunction. Fungi associated infectious diseases have been well recognized in the clinic. However, whether fungi play an important role in non-infectious central nervous system disease is still to be elucidated. Recently, a growing amount of evidence point to a non-negligible role of peripheral fungus in triggering unique inflammation, immune response, and exacerbation of a range of non-infectious CNS disorders, including Multiple sclerosis, Neuromyelitis optica, Parkinson’s disease, Alzheimer’s disease, and Amyotrophic lateral sclerosis et al. In this review, we summarized the recent advances in recognizing patterns and inflammatory signaling of fungi in different subsets of immune cells, with a specific focus on its function in CNS autoimmune and neurodegeneration diseases. In conclusion, the fungus is capable of triggering unique inflammation by multiple mechanisms in the progression of a body of CNS non-infectious diseases, suggesting it serves as a key factor and critical novel target for the development of potential therapeutic strategies

catena-Poly[silver(I)-bis­[μ-bis­(diphenyl­phosphino)methane-κ2 P:P′]-μ-thio­cyanato-κ2 S:S-silver(I)-μ-thio­cyanato-κ2 S:N]

The title compound, [Ag(NCS)(C25H22P2)]n, contains two Ag+ ions, two thio­cyanate ions and two bis­(diphenyl­phosphino)methane (dppm) ligands in the asymmetric unit. One of the thiocyanate ions bridges the two Ag+ ions in a μ2-mode from its S atom and the two dppm ligands bridge the silver ions in a μ1,μ1 mode. The remaining SCN− ion bridges the binuclear units via its N and S atoms, generating a one-dimensional polymer propagating in [01]: the resulting AgP2SN and AgP2S2 coordination geometries could be described as distorted tetra­hedral

(1,10-Phenanthroline-κ2 N,N′)(triphenyl­phosphine-κP)silver(I) trifluoro­methane­sulfonate

The structure of the title complex, [Ag(C12H8N2)(C18H15P)]CF3SO3, is based on a distorted trigonal–planar N2P coordination of the AgI ion, provided by two N atoms of the bidentate phenanthroline ligand and one P atom of the triphenyl­phosphine ligand. The phenanthroline ligand and one phenyl ring of the triphenyl­phosphine ligand almost lie in one plane (maximum deviation = 0.014 Å from the best planes). The crystal structure may be stabilized by an inter­molecular C—H⋯O hydrogen bond between the phenanthroline ligand and the O atom of the trifluoro­methane­sulfonate anion

5,6-Dimethyl-1,2,4-triazin-3-amine

In the crystal structure of the title compound, C5H8N4, adjacent mol­ecules are connected through N—H⋯N hydrogen bonds, resulting in a zigzag chain along [100]. The amino groups and heterocyclic N atoms are involved in further N—H⋯N hydrogen bonds, forming R 2 2(8) motifs

Tetra­aqua­(1,10-phenanthroline-κ2 N,N′)cadmium(II) sulfate dihydrate

In the title mononuclear complex, [Cd(C12H8N2)(H2O)4]SO4·2H2O, the coordination geometry around the CdII atom is a distorted octa­hedron, with two aqua ligands occupying the axial positions. Inter­molecular O—H⋯O hydrogen bonds lead to the formation of a two-dimensional layer structure parallel to (001). The layers are connected by π–π inter­actions between the pyridyl and benzene rings of the phenanthroline ligands [centroid–centroid distances = 3.591 (1) and 3.610 (1) Å]

A tetra­silver(I)ditungsten(VI) cluster with sulfide and bis­(diphenyl­phosphino)methane ligands

The asymmetric unit of the title complex, [Ag4W2S8(C25H22P2)3]·2C3H7NO, tris­[μ2-bis­(diphenyl­phosphino)meth­ane]-3:6κ2 P:P′;4:5κ2 P:P′;5:6κ2 P:P′-μ5-sulfido-2:3:4:5:6κ5 S-μ3-sulfido-1:3:4κ3 S-tetra-μ2-sulfido-1:3κ2 S;1:4κ2 S;2:5κ2 S;2:6κ2 S-disulfido-1κS,2κS-tetra­silver(I)ditungsten(VI) N,N-dimethyl­formamide disolvate, contains two [WS4]2− anions, four silver cations, three bidentate–bridging bis­(diphenyl­phosphino)methane (dppm) ligands and two N,N-dimethyl­formamide (DMF) solvent mol­ecules. The coordination geometry of each Ag atom is distorted tetra­hedral. Two Ag ions are coordinated by μ2-S and μ5-S atoms, and by two P atoms from two dppm ligands, while the other two Ag atoms are coordinated by μ2-S, μ3-S and μ5-S atoms, and by one P atom from a dppm ligand

catena-Poly[[(isoquinoline-κN)(triphenylphospane-κP)copper(I)]-μ-thio­cyanato-κ2 N:S]

In the title coordination compound, [Cu(NCS)(C9H7N)(C18H15P)]n, the CuI atom is tetra­hedrally coordinated by one N atom from an isoquinoline ligand, one P atom from a triphenyl­phospane ligand, and one N and one S atom from two thio­cyanate anions. The thio­cyanide anions bridge the CuI atoms into a chain along [100]. π–π inter­actions between the pyridine and benzene rings of the isoquinoline ligands connect the chains [centroid-to-centroid distance = 3.722 (3) Å]

Tetra­kis(triphenyl­phosphane-κP)silver(I) trifluoro­methane­sulfonate dichloro­methane monosolvate

In the title compound, [Ag(C18H15P)4]CF3O3S·CH2Cl2, the Ag atom is coordinated by four P atoms from four PPh3 ligands. The P—Ag—P angles are in the range 108.02 (6)–110.15 (6)°, which confirms the distorted tetra­hedral environment around the Ag atom