Refined Complexity of PCA with Outliers

Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience. However, it is well-documented that the applicability of PCA in many real scenarios could be constrained by an "immune deficiency" to outliers such as corrupted observations. We consider the following algorithmic question about the PCA with outliers. For a set of $n$ points in $\mathbb{R}^{d}$, how to learn a subset of points, say 1% of the total number of points, such that the remaining part of the points is best fit into some unknown $r$-dimensional subspace? We provide a rigorous algorithmic analysis of the problem. We show that the problem is solvable in time $n^{O(d^2)}$. In particular, for constant dimension the problem is solvable in polynomial time. We complement the algorithmic result by the lower bound, showing that unless Exponential Time Hypothesis fails, in time $f(d)n^{o(d)}$, for any function $f$ of $d$, it is impossible not only to solve the problem exactly but even to approximate it within a constant factor.Comment: To be presented at ICML 201

An Efficient Algorithm for Clustering of Large-Scale Mass Spectrometry Data

High-throughput spectrometers are capable of producing data sets containing thousands of spectra for a single biological sample. These data sets contain a substantial amount of redundancy from peptides that may get selected multiple times in a LC-MS/MS experiment. In this paper, we present an efficient algorithm, CAMS (Clustering Algorithm for Mass Spectra) for clustering mass spectrometry data which increases both the sensitivity and confidence of spectral assignment. CAMS utilizes a novel metric, called F-set, that allows accurate identification of the spectra that are similar. A graph theoretic framework is defined that allows the use of F-set metric efficiently for accurate cluster identifications. The accuracy of the algorithm is tested on real HCD and CID data sets with varying amounts of peptides. Our experiments show that the proposed algorithm is able to cluster spectra with very high accuracy in a reasonable amount of time for large spectral data sets. Thus, the algorithm is able to decrease the computational time by compressing the data sets while increasing the throughput of the data by interpreting low S/N spectra.Comment: 4 pages, 4 figures, Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference o

History of Learning Disabilities: Reflection on the Development of the Concept and Assessment

The history of the concept and identification of Learning Disabilities LD has important stages of development which should be considered by the researchers of this field This development includes different thoughts and experiments which are still controversial until recently This paper discusses this development and divides it into four periods which consider different factors of each period such as the location scholars and critical perspectives and practices Discussion about the impact of the history on the current period is provide

APPEARANCES ARE DECEIVING: LONG-DISTANCE SUBJECT ANAPHORS AND PHASAL BINDING DOMAINS

An unusual behavior of anaphors is to occur in embedded subject positions and bebound across a finite clause boundary by a matrix subject. This thesis, however, demonstrates that such constructions exist in Malki Arabic, besides other languages. First, this thesis shows that the clause size of the embedded clause in which subject anaphors are allowed is CP and not always a TP. Second, in light of current reductionist approaches to binding domains of the classical binding theory to phase theory, a cross-clausal binding relation bears issues to those approaches, as a long-distance antecedence relation crosses a phase boundary. Taking long-distance bound subject anaphors as the main empirical focus in this thesis, I show that the cross-clausal binding relation in Malki Arabic is not bona fide evidence against reducing binding domains to phases. Following Wurmbrand (2019) and Lohninger et al. (2022), I propose that constructions with long-distance bound subject anaphors theoretically resemble cross-clausal A-dependencies, like hyperraising and long-distance agreement, for undergoing movement to a position in the edge of the embedded clause and showing similar properties. Third, I show that reducing binding domains to whole phases is plausible, but taking spell-out domains as binding domains is untenable. Finally, the proposal suggested in this thesis also sheds lights on the possibility of the anaphor agreement effect as an interface condition, in addition to highlighting an account for the accusative-marked embedded subject in Modern Standard Arabic

New inorganic nanomaterials for low-voltage transistor applications

This research aims to synthesise and characterise solution-processable high-k dielectric nanorods, which are potentially suitable for use as the dielectric layer in low-voltage Organic Field-Effect Transistor (OFET) applications. Oleic acid-stabilised titanium dioxide nanorods (TiO₂-OA), metal-doped anatase titanium oxide (TiO₂-OA-M; M=Nb, In, or Nb/In) nanorods, rutile titanium oxide nanorods (TiO₂) and barium titanium oxide nanorods (BaTiO₃) have been prepared and investigated.Solution processable oleic acid-stabilised titanium dioxide nanorods (TiO₂-OA) have been prepared by hydrolysis of titanium (IV) tetraisopropoxide (TTIP) with oleic acid (OA) as surfactant in the presence of trimethylamine N-oxide (TMAO). Furthermore, a series of ligand exchange reactions were carried out to replace the oleic acid bonded on the surface of TiO₂-OA with diethyl 2-phenylethyl phosphonate (DEPPNA), octadecylphosphonic acid (ODPA) or octylphosphonic acid (OPA). The ligand exchange rate was characterised by a combination of 31P liquid NMR, ICP, CHN, and FT-IR. The solubility of the ligand-exchanged products in chlorobenzene was also investigated.A novel method based on the co-hydrolysis of titanium (IV) tetraisopropoxide (TTIP) and niobium or/and indium isopropoxide or ethoxide has been investigated to prepare solution-processable, oleic acid- stabilised, niobium- and indium-doped, anatase TiO₂ nanorods (TiO₂-OA-M; M = Nb, In or Nb/In). The effect of niobium and indium precursors, the molar ratio of Nb or In precursors/TTIP and reaction time on the composition, structure and morphology of the Nb or In doped TiO₂ products have been investigated by a combination of XPS, XRD, ICP, CHN, FT-IR and TEM. Furthermore, a series of ligand exchange reactions were carried out to replace the oleic acid, which is bonded on the surface of TiO₂-OA-M, with diethyl 2-phenylethyl phosphonate (DEPPNA) or octadecylphosphonic acid (ODPA). The solubility of the products in chlorobenzene was also investigated.Rutile titanium dioxide nanorods with different sizes were prepared by three different approaches. In the first approach，hair-like rutile nanorods TiO₂ were prepared by simple hydrolysis of a TiOCl₂ solution at low temperature (50, 70 and 90 °C). In the second approach, rutile nanorods TiO₂ with a length of 150-200 nm and a width of 25-40 nm were prepared by using a hydrothermal treatment of TiOCl₂ at 220 °C. In the third approach, rutile nanorods TiO₂ with length of 80 nm and diameter of 20 nm were prepared by using an hydrothermal reaction of TiOCl₂ in the presence of 3-hydroxytyramine hydrogen chloride, [(HO)₂C₆H₃CH₂CH₂NH₂·HCl] at 150°C. In order to improve the solubility of the obtained rutile titanium dioxide nanorods in organic solvents, different surface-modification methods have been investigated to coat the surface of the rutile titanium dioxide nanorods with various organic ligands. In the first method, a modification of the TiO₂ nanorods with oleic acid (OA) in chlorobenzene was investigated. In the second method, a two-stage treatment of TiO₂ nanorods in an acidic medium was studied, using a selection of oleic acid (OA), diethyl 2-phenylethyl phosphonate (DEPPNA), octylphosphonic acid (OPA) and decylphosphonic acid (ODPA) as ligands. In the third method, wet TiO₂ nanorods before dry was directly modified with a range of oleic acid and amines, e.g., octylamine, dodecylamine and hexadecylamine, as ligands. All the products were characterized by a combination of XRD, ICP, CHN, FT-IR and TEM.The preparation of barium titanium oxide nanorods (BaTiO₃) has been investigated by different approaches. In the first approach, a hydrothermal reaction was carried out to convert the titanium dioxide nanorods prepared in the first and third parts in this research into BaTiO₃ nanorods. The effect of the molar ratio of Ba/Ti, the reaction pH, reaction time and temperature on the composition, structure and morphology of the products were fully investigated. In the second approach, a hydrothermal reaction using a single source Ba/Ti precursor, i.e., barium titanium ethylhexano-isoproxide BaTi(O₂CC₇H₁₅)(OC₃H₇)₅, was carried out to prepare barium titanium oxide nanorods. In the third approach, barium titanium oxide nanorods were prepared by using a hydrothermal reaction between barium chloride (BaCl₂) and titanium oxy chloride (TiOCl₂) in the presence of ethylene glycol as surfactant. All the products have been characterised by a combination of XRD, ICP, CHN, FT-IR and TEM

レーダー・クロス・セクションを用いた円柱形状物質内の水分量推定に関する研究

早大学位記番号:新7736早稲田大