On class visualisation for high dimensional data: Exploring scientific datasets

Parametric Embedding (PE) has recently been proposed as a general-purpose algorithm for class visualisation. It takes class posteriors produced by a mixture-based clustering algorithm and projects them in 2D for visualisation. However, although this fully modularised combination of objectives (clustering and projection) is attractive for its conceptual simplicity, in the case of high dimensional data, we show that a more optimal combination of these objectives can be achieved by integrating them both into a consistent probabilistic model. In this way, the projection step will fulfil a role of regularisation, guarding against the curse of dimensionality. As a result, the tradeoff between clustering and visualisation turns out to enhance the predictive abilities of the overall model. We present results on both synthetic data and two real-world high-dimensional data sets: observed spectra of early-type galaxies and gene expression arrays.Comment: to appear in Lecture notes in Artificial Intelligence vol. 4265, the (refereed) proceedings of the Ninth International conference on Discovery Science (DS-2006), October 2006, Barcelona, Spain. 12 pages, 8 figure

Developments in Correlated Fermions

This manuscript is based on the Summary and Overview talk given at the "The International Conference of Strongly Correlated Electronic Systems" (SCES '04), July 26-30, at Karlsruhe, Germany. After highlighting some of the principal new experimental developments in heavy fermions presented at the conference, I turn to two kinds of theoretical questions. (1) What is understood of the fermi-liquid state of the heavy fermions and what is not, but may reasonably well be understood by systematic calculations. (2) The profound issues raised by the observed correlations near the quantum critical points in the heavy fermions. The numbers and letters in the parenthesis in the text refer to the listing of the talks in the "Program and Abstracts" book of the conference

Sources of intrinsic rotation in the low flow ordering

A low flow, $\delta f$ gyrokinetic formulation to obtain the intrinsic rotation profiles is presented. The momentum conservation equation in the low flow ordering contains new terms, neglected in previous first principles formulations, that may explain the intrinsic rotation observed in tokamaks in the absence of external sources of momentum. The intrinsic rotation profile depends on the density and temperature profiles and on the up-down asymmetry.Comment: 20 page

Spin Gap Fixed Points in the Double Chain Problem

Applying the bosonization procedure to weakly coupled Hubbard chains we discuss the fixed points of the renormalization group flow where all spin excitations are gapful and a singlet pairing becomes the dominant instability.Comment: 15 pages, TeX, C Version 3.

Fermi surface renormalization in Hubbard ladders

We derive the one-loop renormalization equations for the shift in the Fermi-wavevectors for one-dimensional interacting models with four Fermi-points (two left and two right movers) and two Fermi velocities v_1 and v_2. We find the shift to be proportional to (v_1-v_2)U^2, where U is the Hubbard-U. Our results apply to the Hubbard ladder and to the t_1-t_2 Hubbard model. The Fermi-sea with fewer particles tends to empty. The stability of a saddle point due to shifts of the Fermi-energy and the shift of the Fermi-wavevector at the Mott-Hubbard transition are discussed.Comment: 5 pages, 4 Postscript figure

Charge Dynamics in the Planar t-J Model

The finite-temperature optical conductivity $\sigma(\omega)$ in the planar $t-J$ model is analysed using recently introduced numerical method based on the Lanczos diagonalization of small systems (up to 20 sites), as well as by analytical approaches, including the method of frequency moments and the retraceable-path approximation. Results for a dynamical mobility of a single hole at elevated temperatures $T>t$ reveal a Gaussian-like $\mu(\omega)$ spectra, however with a nonanalytical behavior at low $\omega$. In the single hole response a difference between the ferromagnetic (J=0) and the antiferromagnetic ($J>0$) polaron shows up at $T<J$. At larger dopings numerical results in studied systems are consistent with the thermodynamical behavior for $T>T^*\ge 0.1~t$. $\sigma(\omega)$ spectra show a non-Drude falloff at large frequencies. In particular for `optimum' doping $n_h \sim 0.2$ we obtain in the low-$\omega,T$ regime the relaxation rate $\tau^{-1} \sim 0.6 (\omega+\xi T)$ with $\xi \sim 3$, being consistent with the marginal Fermi liquid concept and experiments. Within the same regime we reproduce the nearly linear variation of dc resistivity $\rho$ with $T$. This behavior is weakly dependent on $J$, provided that $J<t$.Comment: 21 pages of text plus 17 figures, postscrip

Pharmacokinetic profile and quantitation of protection against soman poisoning by the antinicotinic compound MB327 in the guinea-pig

Current organophosphorus nerve agent medical countermeasures do not directly address the nicotinic effects of poisoning. A series of antinicotinic bispyridinium compounds has been synthesized in our laboratory and screened in vitro. Their actions can include open-channel block at the nicotinic receptor which may contribute to their efficacy. The current lead compound from these studies, MB327 1,1′-(propane-1,3-diyl)bis(4-tert-butylpyridinium) as either the diiodide (I2) or dimethanesulfonate (DMS) has been examined in vivo for efficacy against nerve agent poisoning. MB327 I2 (0–113 mg kg−1) or the oxime HI-6 DMS (0–100 mg kg− 1), in combination with atropine and avizafone (each at 3 mg kg−1) was administered to guinea-pigs 1 min following soman poisoning. Treatment increased the LD50 of soman in a dose-dependent manner. The increase was statistically significant (p < 0.01) at the 33.9 mg kg−1 (MB327) or 30 mg kg−1 (HI-6) dose with a comparable degree of protection obtained for both compounds. Following administration of 10 mg kg−1 (i.m.), MB327 DMS reached plasma Cmax of 22 μM at 12 min with an elimination t1/2 of 22 min. In an adverse effect study, in the absence of nerve agent poisoning, a dose of 100 mg kg−1 or higher of MB327 DMS was lethal to the guinea-pigs. A lower dose of MB327 DMS (30 mg kg−1) caused flaccid paralysis accompanied by respiratory impairment. Respiration normalised by 30 min, although the animals remained incapacitated to 4 h. MB327 or related compounds may be of utility in treatment of nerve agent poisoning as a component of therapy with atropine, anticonvulsant and oxime, or alternatively as an infusion under medical supervision

Thirty Years of heavy Fermions: Scientific Setting for their Discovery and Partial Understanding

Heavy-Fermions provide an extreme example of the utility of the idea of continuity and analyticity in physics. Their discovery and study in the past thirty years has added a fascinating chapter to condensed matter physics. I briefly review the origins of the heavy-fermion problem out of the study of magnetic moments in metals and the study of mixed-valent rare-earth compounds. I also review the principal ideas underlying the features understood in their fermi-liquid phase as well as in their anisotropic superconductivity. The unsolved issues are also briefly mentioned.Comment: This is the text of one of the talks given at the plenary symposium entitled "Thirty years of heavy Fermions" at the beginning of the International conference on Strongly correlated Electrons in Vienna in July 200

Competing Orders in Coupled Luttinger Liquids

We consider the problem of two coupled Luttinger liquids both at half filling and at low doping levels, to investigate the problem of competing orders in quasi-one-dimensional strongly correlated systems. We use bosonization and renormalization group equations to investigate the phase diagrams, to determine the allowed phases and to establish approximate boundaries among them. Because of the chiral translation and reflection symmetry in the charge mode away from half filling, orders of charge density wave (CDW) and spin-Peierls (SP) diagonal current (DC) and $d$-density wave (DDW) form two doublets and thus can be at most quasi-long range ordered. At half-filling, umklapp terms break this symmetry down to a discrete group and thus Ising-type ordered phases appear as a result of spontaneous breaking of the residual symmetries. Quantum disordered Haldane phases are also found, with finite amplitudes of pairing orders and triplet counterparts of CDW, SP, DC and DDW. Relations with recent numerical results and implications to similar problems in two dimensions are discussed.Comment: 16 pages, 5 figures, 4 tables. Revised manuscript; a misprint in Eq. B3 has been corrected. The paper is already in print in PR

Role of Orbital Degeneracy in Double Exchange Systems

We investigate the role of orbital degeneracy in the double exchange (DE) model. In the $J_{H}\to\infty$ limit, an effective generalized ``Hubbard'' model incorporating orbital pseudospin degrees of freedom is derived. The model possesses an exact solution in one- and in infinite dimensions. In 1D, the metallic phase off ``half-filling'' is a Luttinger liquid with pseudospin-charge separation. Using the $d=\infty$ solution for our effective model, we show how many experimental observations for the well-doped ($x\simeq 0.3$) three-dimensional manganites $La_{1-x}Sr_{x}MnO_{3}$ can be qualitatively explained by invoking the role of orbital degeneracy in the DE model.Comment: 8 pages, 2 figures, submitted to Phys. Rev.