Hodge theory and derived categories of cubic fourfolds

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3s associated to them at the level of derived categories. These two notions of having an associated K3 should coincide. We prove that they coincide generically: Hassett's cubics form a countable union of irreducible Noether-Lefschetz divisors in moduli space, and we show that Kuznetsov's cubics are a dense subset of these, forming a non-empty, Zariski open subset in each divisor.Comment: 37 pages. Applications to algebraic cycles added, and other improvements following referees' suggestions. This is a slightly expanded version of the paper to appear in Duke Math

Studying Intermediate pT Hadron Production with Fluctuations

Mechanisms for particle production at intermediate pT in nuclear collisions at RHIC are discussed, emphasizing the differences in associated jet-like correlations between color-neutral and colored production. An alternative production mechanism involving both recombination and fragmentation is suggested, which might simultaneously lead to an enhancement of baryons and to jet-like correlations. To gain more insight into the relative importance of different mechanisms a study of constrained distributions of associated multiplicity is proposed. In a simple model it is shown that these multiplicity distributions may change significantly, if the nature of the production mechanism fluctuates from event to event.Comment: 7 pages, 4 figures, talk at Hot Quarks 2004 conferenc

The state of our interstates

President Obama's budget proposal emphasizes the importance of infrastructure investments for the nation's economic health, so now seems a good time to assess the condition of our country's major roads.Express highways

Computing Groebner Fans

This paper presents algorithms for computing the Groebner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Groebner bases of the ideal. Our algorithms are based on a uniform definition of the Groebner fan that applies to both homogeneous and non-homogeneous ideals and a proof that this object is a polyhedral complex. We show that the cells of a Groebner fan can easily be oriented acyclically and with a unique sink, allowing their enumeration by the memory-less reverse search procedure. The significance of this follows from the fact that Groebner fans are not always normal fans of polyhedra in which case reverse search applies automatically. Computational results using our implementation of these algorithms in the software package Gfan are included.Comment: 26 page

Minimal Pati-Salam Model from String Theory Unification

We provide what we believe is the minimal three family ${\cal N} = 1$ SUSY and conformal Pati-Salam Model from type IIB superstring theory. This $Z_3$ orbifolded AdS$\otimes S^5$ model has long lived protons and has potential phenomenological consequences for LHC.Comment: 8 page

Towards a Novel no-hair Theorem for Black Holes

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.Comment: 25 pages, 11 figure

Momentum transfer dependence of the proton's electric and magnetic polarizabilities

The Q^2-dependence of the sum of the electric and magnetic polarizabilities of the proton is calculated over the range 0 \leq Q^2 \leq 6 GeV^2 using the generalized Baldin sum rule. Employing a parametrization of the F_1 structure function valid down to Q^2 = 0.06 GeV^2, the polarizabilities at the real photon point are found by extrapolating the results of finite Q^2 to Q^2 = 0 GeV^2. We determine the evolution over four-momentum transfer to be consistent with the Baldin sum rule using photoproduction data, obtaining \alpha + \beta = 13.7 \pm 0.7 \times 10^{-4}\, \text{fm}^3.Comment: 4 pages, 3 figure

Reduced CD40L expression on ex vivo activated CD4+T-lymphocytes from patients with excellent renal allograft function measured with a rapid whole blood flow cytometry procedure

Background: The CD40-CD40L (CD154) costimulatory pathway plays a critical role in the pathogenesis of kidney allograft rejection. In renal transplant biopsies, CD4+ CD40L+ graft-infiltrating cells were detected during chronic rejection in contrast to acute rejection episodes. Using a rapid noninvasive FACS procedure, we were able to demonstrate CD40L upregulation in peripheral blood of patients with chronic renal allograft dysfunction. Materials and Methods: Whole blood from recipients of renal allografts was stimulated with PMA and ion-omycin and measured by flow cytometry. Patients were assigned to three groups based on transplant function. Group 1: 26 patients with excellent renal transplant function; group 2: 28 patients with impaired transplant function; group 3: 14 patients with chronic allograft dysfunction and group 4: 8 healthy controls. Results: The median percentage +/-SEM of CD4+/ CD40L+ cells stimulated ex vivo at 10 ng/ml PMA was as follows: group 1: 28.3 +/- 4.1%; group 2: 18.4 +/- 2.4%; group 3: 50.1 +/- 5.0% and group 4: 40.4 +/- 3.4%. Subdivisions of groups 2 and 3 resulted in different CD40L expression patterns. Patients with increased serum creatinine since the initial phase after transplantation ( groups 2a and 3a) revealed a higher percentage of CD4+ CD40L+ cells than patients showing a gradual increase over time ( groups 2b and 3b). Consequently, patients of group 3a exhibited a significantly reduced transplant function compared with those of group 3b. Conclusion: After PMA + ionomycin stimulation, patients with excellent kidney graft function displayed significantly reduced expression of CD40L surface molecules on CD4+ cells early after transplantation. Those with a chronic dysfunction of the renal graft showed significantly more CD4+ cells expressing CD40L compared to the other transplanted groups. These results demonstrate that the percentage of CD4+ CD40L+ cells stimulated ex vivo in peripheral blood may be a valuable marker for chronic allograft nephropathy. Copyright (C) 2004 S. Karger AG, Basel