The topology of spaces of polygons

Let $E_{d}(\ell)$ denote the space of all closed $n$-gons in $\R^{d}$ (where $d\ge 2$) with sides of length $\ell_1,..., \ell_n$, viewed up to translations. The spaces $E_d(\ell)$ are parameterized by their length vectors $\ell=(\ell_1,..., \ell_n)\in \R^n_{>}$ encoding the length parameters. Generically, $E_{d}(\ell)$ is a closed smooth manifold of dimension $(n-1)(d-1)-1$ supporting an obvious action of the orthogonal group ${O}(d)$. However, the quotient space $E_{d}(\ell)/{O}(d)$ (the moduli space of shapes of $n$-gons) has singularities for a generic $\ell$, assuming that $d>3$; this quotient is well understood in the low dimensional cases $d=2$ and $d=3$. Our main result in this paper states that for fixed $d\ge 3$ and $n\ge 3$, the diffeomorphism types of the manifolds $E_{d}(\ell)$ for varying generic vectors $\ell$ are in one-to-one correspondence with some combinatorial objects -- connected components of the complement of a finite collection of hyperplanes. This result is in the spirit of a conjecture of K. Walker who raised a similar problem in the planar case $d=2$

Nuclear physics from strong coupling QCD

The strong coupling limit (beta_gauge = 0) of QCD offers a number of remarkable research possibilities, of course at the price of large lattice artifacts. Here, we determine the complete phase diagram as a function of temperature T and baryon chemical potential mu_B, for one flavor of staggered fermions in the chiral limit, with emphasis on the determination of a tricritical point and on the T ~ 0 transition to nuclear matter. The latter is known to happen for mu_B substantially below the baryon mass, indicating strong nuclear interactions in QCD at infinite gauge coupling. This leads us to studying the properties of nuclear matter from first principles. We determine the nucleon-nucleon potential in the strong coupling limit, as well as masses m_A of nuclei as a function of their atomic number A. Finally, we clarify the origin of nuclear interactions at strong coupling, which turns out to be a steric effect.Comment: 8 pages, 4 figures. Presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin

Strong coupling effective theory with heavy fermions

We extend the recently developed strong coupling, dimensionally reduced Polyakov-loop effective theory from finite-temperature pure Yang-Mills to include heavy fermions and nonzero chemical potential by means of a hopping parameter expansion. Numerical simulation is employed to investigate the weakening of the deconfinement transition as a function of the quark mass. The tractability of the sign problem in this model is exploited to locate the critical surface in the (M/T, mu/T, T) space over the whole range of chemical potentials from zero up to infinity.Comment: 7 pages, 5 figures. Proceeding for the XXIX International Symposium on Lattice Field Theory (Lattice 2011), Squaw Valley, Lake Tahoe, California, July 10-16, 201

The QCD deconfinement transition for heavy quarks and all baryon chemical potentials

Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N_\tau\sim 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.Comment: 24 pages, 17 figure

Effective theory for QCD at finite temperature and density from strong coupling expansion

QCD at finite temperature and denisty remains intractable by Monte Carlo simulations for quark chemical potentials m >∼T. It has been a long standing problem to derive effective theories from QCD which describe the phase structure of the former with controlled errors. We propose a solution to this problem by a combination of analytical and numerical methods. Starting from lattice QCD with in Wilson’s formulation, we derive an effective action in terms of Polyakov loops by means of combined strong coupling and hopping expansions. The theory correctly reflects the centre-symmetry in the pure gauge limit and its breaking through quarks. It is valid for heavy quarks and lattices up to Nt ∼ 6. Its sign problem can be solved and we are able to calculate the deconfinement transition of QCD with heavy quarks for all chemical potentials

Tilivalline- and Tilimycin-Independent Effects of Klebsiella oxytoca on Tight Junction-Mediated Intestinal Barrier Impairment

Klebsiella oxytoca causes antibiotic-associated hemorrhagic colitis and diarrhea. This was attributed largely to its secreted cytotoxins tilivalline and tilimycin, inductors of epithelial apoptosis. To study whether Klebsiella oxytoca exerts further barrier effects, T84 monolayers were challenged with bacterial supernatants derived from tilivalline/tilimycin-producing AHC6 or its isogeneic tilivalline/tilimycin-deficient strain Mut-89. Both preparations decreased transepithelial resistance, enhanced fluorescein and FITC-dextran-4kDa permeabilities, and reduced expression of barrier-forming tight junction proteins claudin-5 and -8. Laser scanning microscopy indicated redistribution of both claudins off the tight junction region in T84 monolayers as well as in colon crypts of mice infected with AHC6 or Mut-89, indicating that these effects are tilivalline/tilimycin-independent. Furthermore, claudin-1 was affected, but only in a tilivalline/tilimycin-dependent manner. In conclusion, Klebsiella oxytoca induced intestinal barrier impairment by two mechanisms: the tilivalline/tilimycin-dependent one, acting by increasing cellular apoptosis and a tilivalline/tilimycin-independent one, acting by weakening the paracellular pathway through the tight junction proteins claudin-5 and -8

ATX1/AtCOMPASS and the H3K4me3 Marks: How Do They Activate \u3ci\u3eArabidopsis\u3c/i\u3e Genes?

Despite the proven correlation between gene transcriptional activity and the levels of tri-methyl marks on histone 3 lysine4 (H3K4me3) of their nucleosomes, whether H3K4me3 contributes to, or “registers,” activated transcription is still controversial. Other questions of broad relevance are whether histone-modifying proteins are involved in the recruitment of Pol II and the general transcription machinery and whether they have roles other than their enzyme activities. We address these questions as well as the roles of the ARABIDOPSIS HOMOLOG OF TRITHORAX1 (ATX1), of the COMPASS-related (AtCOMPASS) protein complex, and of their product, H3K4me3, at ATX1-dependent genes. We suggest that the ambiguity about the role of H3K4me3 as an activating mark is because of the unknown duality of the ATX1/AtCOMPASS to facilitate PIC assembly and to generate H3K4me3, which is essential for activating transcriptional elongation

ATX1/AtCOMPASS and the H3K4me3 Marks: How Do They Activate \u3ci\u3eArabidopsis\u3c/i\u3e Genes?

Despite the proven correlation between gene transcriptional activity and the levels of tri-methyl marks on histone 3 lysine4 (H3K4me3) of their nucleosomes, whether H3K4me3 contributes to, or “registers,” activated transcription is still controversial. Other questions of broad relevance are whether histone-modifying proteins are involved in the recruitment of Pol II and the general transcription machinery and whether they have roles other than their enzyme activities. We address these questions as well as the roles of the ARABIDOPSIS HOMOLOG OF TRITHORAX1 (ATX1), of the COMPASS-related (AtCOMPASS) protein complex, and of their product, H3K4me3, at ATX1-dependent genes. We suggest that the ambiguity about the role of H3K4me3 as an activating mark is because of the unknown duality of the ATX1/AtCOMPASS to facilitate PIC assembly and to generate H3K4me3, which is essential for activating transcriptional elongation

Towards corrections to the strong coupling limit of staggered lattice QCD

We report on the first steps of an ongoing project to add gauge observables and gauge corrections to the well-studied strong coupling limit of staggered lattice QCD, which has been shown earlier to be amenable to numerical simulations by the worm algorithm in the chiral limit and at finite density. Here we show how to evaluate the expectation value of the Polyakov loop in the framework of the strong coupling limit at finite temperature, allowing to study confinement properties along with those of chiral symmetry breaking. We find the Polyakov loop to rise smoothly, thus signalling deconfinement. The non-analytic nature of the chiral phase transition is reflected in the derivative of the Polyakov loop. We also discuss how to construct an effective theory for non-zero lattice coupling, which is valid to $O(\beta)$.Comment: 7 pages, 4 figures, Talk presented at the XXIX International Symposium on Lattice Field Theory, Lattice2011, Squaw Valley, Lake Tahoe, California, July 201