GAPS IN THE HEISENBERG-ISING MODEL

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at special values of the anisotropy $\Delta= \cos(\pi/Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $\Delta$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $\Delta\sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and the corresponding perturbation expansion in $\Delta$ shows a remarkable cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques

Resolving the electron temperature discrepancies in HII Regions and Planetary Nebulae: kappa-distributed electrons

The measurement of electron temperatures and metallicities in H ii regions and Planetary Nebulae (PNe) has-for several decades-presented a problem: results obtained using different techniques disagree. What it worse, they disagree consistently. There have been numerous attempts to explain these discrepancies, but none has provided a satisfactory solution to the problem. In this paper, we explore the possibility that electrons in H ii regions and PNe depart from a Maxwell-Boltzmann equilibrium energy distribution. We adopt a "kappa-distribution" for the electron energies. Such distributions are widely found in Solar System plasmas, where they can be directly measured. This simple assumption is able to explain the temperature and metallicity discrepancies in H ii regions and PNe arising from the different measurement techniques. We find that the energy distribution does not need to depart dramatically from an equilibrium distribution. From an examination of data from Hii regions and PNe it appears that kappa ~ 10 is sufficient to encompass nearly all objects. We argue that the kappa-distribution offers an important new insight into the physics of gaseous nebulae, both in the Milky Way and elsewhere, and one that promises significantly more accurate estimates of temperature and metallicity in these regions.Comment: 16 pages, 11 figures, 2 tables, published in Ap

Targeting cyclin-dependent kinase 1 (CDK1) but not CDK4/6 or CDK2 is selectively lethal to MYC-dependent human breast cancer cells

Background Although MYC is an attractive therapeutic target for breast cancer treatment, it has proven challenging to inhibit MYC directly, and clinically effective pharmaceutical agents targeting MYC are not yet available. An alternative approach is to identify genes that are synthetically lethal in MYC-dependent cancer. Recent studies have identified several cell cycle kinases as MYC synthetic-lethal genes. We therefore investigated the therapeutic potential of specific cyclin-dependent kinase (CDK) inhibition in MYC-driven breast cancer. Methods Using small interfering RNA (siRNA), MYC expression was depleted in 26 human breast cancer cell lines and cell proliferation evaluated by BrdU incorporation. MYC-dependent and MYC-independent cell lines were classified based on their sensitivity to siRNA-mediated MYC knockdown. We then inhibited CDKs including CDK4/6, CDK2 and CDK1 individually using either RNAi or small molecule inhibitors, and compared sensitivity to CDK inhibition with MYC dependence in breast cancer cells. Results Breast cancer cells displayed a wide range of sensitivity to siRNA-mediated MYC knockdown. The sensitivity was correlated with MYC protein expression and MYC phosphorylation level. Sensitivity to siRNA-mediated MYC knockdown did not parallel sensitivity to the CDK4/6 inhibitor PD0332991; instead MYC-independent cell lines were generally sensitive to PD0332991. Cell cycle arrest induced by MYC knockdown was accompanied by a decrease in CDK2 activity, but inactivation of CDK2 did not selectively affect the viability of MYC-dependent breast cancer cells. In contrast, CDK1 inactivation significantly induced apoptosis and reduced viability of MYC-dependent cells but not MYC- independent cells. This selective induction of apoptosis by CDK1 inhibitors was associated with up-regulation of the pro-apoptotic molecule BIM and was p53-independent. Conclusions Overall, these results suggest that further investigation of CDK1 inhibition as a potential therapy for MYC-dependent breast cancer is warranted.</p

Structural determination of archaeal UDP-N-acetylglucosamine 4-epimerase from Methanobrevibacter ruminantium M1 in complex with the bacterial cell wall intermediate UDP-N-acetylmuramic acid

The crystal structure of UDP-N-acetylglucosamine 4-epimerase (UDP-GlcNAc 4-epimerase; WbpP; EC 5.1.3.7), from the archaeal methanogen Methanobrevibacter ruminantium strain M1, was determined to a resolution of 1.65 Å. The structure, with a single monomer in the crystallographic asymmetric unit, contained a conserved N-terminal Rossmann fold for nucleotide binding and an active site positioned in the C-terminus. UDP-GlcNAc 4-epimerase is a member of the short-chain dehydrogenase/reductase superfamily, sharing sequence motifs and structural elements characteristic of this family of oxidoreductases and bacterial 4-epimerases. The protein was co-crystallized with coenzyme NADH and UDP-N-acetylmuramic acid, the latter an unintended inclusion and well known product of the bacterial enzyme MurB and a critical intermediate for bacterial cell wall synthesis. This is a non-native UDP sugar amongst archaea and was most likely incorporated from the Eschericha coli expression host during purification of the recombinant enzyme

Universal Level dynamics of Complex Systems

. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of basis. It turns out that, in the case (i), a redefinition of the parameter governing the evolution leads to a Fokker-Planck equation similar to the one obtained when the perturbation is taken from a standard Gaussian ensemble (with invariant measure). This equivalence can therefore help us to obtain the correlations for various physically-significant cases modeled by generalized Gaussian ensembles by using the already known correlations for standard Gaussian ensembles. For large $N$-values, our results for both cases (i) and (ii) are similar to those obtained for Wigner-Dyson gas as well as for the perturbation taken from a standard Gaussian ensemble. This seems to suggest the independence of evolution, in thermodynamic limit, from the nature of perturbation involved as well as the initial conditions and therefore universality of dynamics of the eigenvalues of complex systems.Comment: 11 Pages, Latex Fil

Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model

We consider a quantum moany-body problem in one-dimension described by a Jastrow type, characterized by an exponent $\lambda$ and a parameter $\gamma$. We show that with increasing $\gamma$, the Fermi Liquid state ($\gamma=0)$ crosses over to non-Fermi liquid states, characterized by effective "temperature".Comment: 8pp. late

Solutions to the Multi-Component 1/R Hubbard Model

In this work we introduce one dimensional multi-component Hubbard model of 1/r hopping and U on-site energy. The wavefunctions, the spectrum and the thermodynamics are studied for this model in the strong interaction limit $U=\infty$. In this limit, the system is a special example of $SU(N)$ Luttinger liquids, exhibiting spin-charge separation in the full Hilbert space. Speculations on the physical properties of the model at finite on-site energy are also discussed.Comment: 9 pages, revtex, Princeton-May1