Simple and Effective Visual Models for Gene Expression Cancer Diagnostics

In the paper we show that diagnostic classes in cancer gene expression data sets, which most often include thousands of features (genes), may be effectively separated with simple two-dimensional plots such as scatterplot and radviz graph. The principal innovation proposed in the paper is a method called VizRank, which is able to score and identify the best among possibly millions of candidate projections for visualizations. Compared to recently much applied techniques in the field of cancer genomics that include neural networks, support vector machines and various ensemble-based approaches, VizRank is fast and finds visualization models that can be easily examined and interpreted by domain experts. Our experiments on a number of gene expression data sets show that VizRank was always able to find data visualizations with a small number of (two to seven) genes and excellent class separation. In addition to providing grounds for gene expression cancer diagnosis, VizRank and its visualizations also identify small sets of relevant genes, uncover interesting gene interactions and point to outliers and potential misclassifications in cancer data sets

VizRank: Data Visualization Guided by Machine Learning

Data visualization plays a crucial role in identifying interesting patterns in exploratory data analysis. Its use is, however, made difficult by the large number of possible data projections showing different attribute subsets that must be evaluated by the data analyst. In this paper, we introduce a method called VizRank, which is applied on classified data to automatically select the most useful data projections. VizRank can be used with any visualization method that maps attribute values to points in a two-dimensional visualization space. It assesses possible data projections and ranks them by their ability to visually discriminate between classes. The quality of class separation is estimated by computing the predictive accuracy of k-nearest neighbor classifier on the data set consisting of x and y positions of the projected data points and their class information. The paper introduces the method and presents experimental results which show that VizRank's ranking of projections highly agrees with subjective rankings by data analysts. The practical use of VizRank is also demonstrated by an application in the field of functional genomics

The Chaotropically Synthesized Dimolybdenum(II,II) Compound

A non-classic approach in the synthesis and crystal growth within electrostricted water solutions of highly charged ionic species allowed us to obtain bright monocrystals of the zwitterionic tetracarboxylate compound Mo2(O2CC6H3(NH3)2)4Cl8 16H2O (1). The title compound tetrakis-(-3,5-diaminobenzoate)octachlorodimolybdenum(II,II)—aqua(1/16) (1) crystallizes in the P21/c monoclinic space group with a = 11.0825(13) Å, b = 23.983(3) Å, c = 10.935(6) Å, = 103.04(3)°, and Z = 2. Proton jumps between aromatic NH3+ and the neighbouring contacting groups H2O or Cl– of (1) increase the extent of donor (p–) interactions from equatorial oxygen atoms to the central dimolybdenum(II,II) core. Existence of unequivalent carboxylate ligands with different binding affinity around the Mo2 4+ dimer is indicated. The structure of the reference compound 3,5-diaminobenzoic acid—bis(hydrogen chloride)—hemihydrate 3,5-(H2N)2C6H3CO2H 2HCl 1/2H2O (2) was solved and compared with the structural data of (1). Triclinic needles of (2) crystallize in the P1 space group with a = 8.695(2) Å, b = 9.768(2) Å, c = 13.779(3) Å, α = 67.43(2), β = 68.69(2), γ = 72.66(2)° and Z = 4

Behaviour of Dimolyhdenum Tetraacetate in Aqueous Solutions of Hydrogen Halides. Synthesis and Crystal Structures of (pyH)2[Mo2(02CCH3)4Br2] and two Modifications of (pyH)2[Mo2(02CCH3 )4I2] (py =pyridine)

The axial diadducts (pyH)2[Mo2(02CCHa)4X2], (py =pyridine, X = Br, I) were isolated from solutions of dimolybdenum tetra- • acetate in HX 1 : 1 after addition of pyridinium halide. (pyH)2 [Mo2(02CCHa)4Br2] (A) crystallizes in the space group I4/m with a= 0.9746(2) nm, c = 1.3948(2) nm, V = 1.32484 nma and Z = 2. Two modifications of the iodide analog were isolated. Triclinic modification (B) crystallizes in the space group Pl with a= 1.0016(1) nm, b = 1.0092(2) nm, c = 1.6325(2) nm, a = 74.75(1)0 , fJ = 71.38(2) 0 , r = 61.12(2)0 , V = 1.35747 nm3 mid Z = 2; tetragonal modification (C) in the space group I4/mcm with a = 1.3086(1) nm, c = 1.4712(1) nm, V = 2.51933 nm3 and Z = 4. The Mo - X (X = Br, I) distances, found in anions [Mo2(02CCH3)4X2]2-, 287.9(3) pm in A, 326.2(1) pm and 329.9(1) pm in B, and 320.4(1) pm in C are quite long, indicating only weak axial coordination. Accordingly, the Mo - Mo distances 210.2(1) pm in A, 210.3(1) pm in B, and 210.2(1) pm in C are only slightly longer than the Mo - Mo distance of 209.3(1) pm found in Mo2(02CCHa)4

Behaviour of Dimolyhdenum Tetraacetate in Aqueous Solutions of Hydrogen Halides. Synthesis and Crystal Structures of (pyH)2[Mo2(02CCH3)4Br2] and two Modifications of (pyH)2[Mo2(02CCH3 )4I2] (py =pyridine)

The axial diadducts (pyH)2[Mo2(02CCHa)4X2], (py =pyridine, X = Br, I) were isolated from solutions of dimolybdenum tetra- • acetate in HX 1 : 1 after addition of pyridinium halide. (pyH)2 [Mo2(02CCHa)4Br2] (A) crystallizes in the space group I4/m with a= 0.9746(2) nm, c = 1.3948(2) nm, V = 1.32484 nma and Z = 2. Two modifications of the iodide analog were isolated. Triclinic modification (B) crystallizes in the space group Pl with a= 1.0016(1) nm, b = 1.0092(2) nm, c = 1.6325(2) nm, a = 74.75(1)0 , fJ = 71.38(2) 0 , r = 61.12(2)0 , V = 1.35747 nm3 mid Z = 2; tetragonal modification (C) in the space group I4/mcm with a = 1.3086(1) nm, c = 1.4712(1) nm, V = 2.51933 nm3 and Z = 4. The Mo - X (X = Br, I) distances, found in anions [Mo2(02CCH3)4X2]2-, 287.9(3) pm in A, 326.2(1) pm and 329.9(1) pm in B, and 320.4(1) pm in C are quite long, indicating only weak axial coordination. Accordingly, the Mo - Mo distances 210.2(1) pm in A, 210.3(1) pm in B, and 210.2(1) pm in C are only slightly longer than the Mo - Mo distance of 209.3(1) pm found in Mo2(02CCHa)4

The Chaotropically Synthesized Dimolybdenum(II,II) Compound

A non-classic approach in the synthesis and crystal growth within electrostricted water solutions of highly charged ionic species allowed us to obtain bright monocrystals of the zwitterionic tetracarboxylate compound Mo2(O2CC6H3(NH3)2)4Cl8 16H2O (1). The title compound tetrakis-(-3,5-diaminobenzoate)octachlorodimolybdenum(II,II)—aqua(1/16) (1) crystallizes in the P21/c monoclinic space group with a = 11.0825(13) Å, b = 23.983(3) Å, c = 10.935(6) Å, = 103.04(3)°, and Z = 2. Proton jumps between aromatic NH3+ and the neighbouring contacting groups H2O or Cl– of (1) increase the extent of donor (p–) interactions from equatorial oxygen atoms to the central dimolybdenum(II,II) core. Existence of unequivalent carboxylate ligands with different binding affinity around the Mo2 4+ dimer is indicated. The structure of the reference compound 3,5-diaminobenzoic acid—bis(hydrogen chloride)—hemihydrate 3,5-(H2N)2C6H3CO2H 2HCl 1/2H2O (2) was solved and compared with the structural data of (1). Triclinic needles of (2) crystallize in the P1 space group with a = 8.695(2) Å, b = 9.768(2) Å, c = 13.779(3) Å, α = 67.43(2), β = 68.69(2), γ = 72.66(2)° and Z = 4

Synthesis, Characterization and Reactions of Compounds, Containing Anion [Mo2Br8H]3-. Crystal Structure of (pipH)3[Mo2Br8H] (pip = piperidine)

Preparation and characterization of (pyH)3[Mo2Br8H] (py = pyridine) (1), (pipH)3[Mo2BrgH] (pip=piperidine) (2), and (morphH)2(H703)[Mo2Br8H] (morph=morpholine (3) are described. (pipH)3[Mo2Br8H] (2) crystallizes in the monoclinic space group P2jc with a = 15.378(4), b = 12.149(7), c = 16.870(5) Å, p = 107.40(2)° and Z = 4; 1855 data with I > 3oil) were refined to R = 0.069, Rw = 0.073. The structure of erystallographically asymmetric [Mo2Br8H]3~ anion revealed a greater trans effect of the p-ñ than that of the /i-Br, found also in the case of other [Mo2X8H]3“, X = Cl, Br, I anions. Two reaction pathways dominate the chemistry of compounds containing [Mo2Br8H]3_, as found in the studies of reactions with pyridine, HBr(aq) and CH3COOH(aq) and they can be represented schematically as (a) Mof + H“ + H+ -> Mof + H2, and (b) Mof + H~ -» Mof + H+

The Crystal Structure of Ammonium Hydrogen Maleate

Ammonium hydrogen maleate, NH4+C4Ha04- crystallizes in the orthorhombic system with a = 0.4616(1), b = 0.8085(2), c = 1.6410(5) nm, Z = 4 in space group Pbcm, and is isostructural with the analogous potassium salt. The crystal structure has been refined from diffracton1eter data to conventional R and Rw of 0.052 and 0.065 for 690 reflexions [I> 3 a (I)]. Minor changes in the crystal struc-· ture were observed due to formation of N-H · · · 0 hydrogen bonds

VizRank: Finding Informative Data Projections in Functional Genomics by Machine Learning

VizRank is a tool that finds interesting two-dimensional projections of class-labeled data. When applied to multi-dimensional functional genomics data sets, VizRank can systematically find relevant biological patterns

Two Types of Pyridine Ligands in Mononuclear and Dinuclear Copper(II) Carboxylates

Copper(II) acetate [Cu(OOCCH3)2(L1)2] (L1 = 2,6-diaminopyridine) (1), [Cu(OOCCH3)2(L2)2] (L2 = 2-amino-6-methylpyridine) (2) and benzoate compounds [Cu2(OOCC6H5)4(L1)2]·2CH3CN (3), [Cu2(OOCC6H5)4(L1)2] (4), [Cu2(OOCC6H5)4(L2)2] (5), [Cu(OOCC6H5)2(L2)2] (6), were synthesized and characterized. X-ray structure analysis revealed monomeric structure in 1 and 6. In 1, cis arrangement of the ligands was found, and trans in 6, in an elongated octahedral CuO4N2 chromophore. The basal plane in 1 and 6 is formed by one co-ordinated oxygen atom from both carboxylates (Cu–O 1.9560(12)–2.007(3) Å) and pyridine nitrogen atom from two pyridine ligands (Cu–N 2.013(3)–2.282(14) Å), forming a CuO2N2 plane, while the second carboxylate oxygen atoms are more distant (Cu–O 2.488(3)–2.7648(16) Å). The dinuclear paddle- wheel central core was found in 5 (Cu–O 1.942(6)–1.992(6) Å), with pyridine nitrogen atoms in the axial positions (Cu–N 2.283(7), 2.284(7) Å). All compounds were characterized by magnetic measurements, electronic and vibrational spectroscopy and tested for fungal growth retardation activity