Logarithmic intertwining operators and vertex operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra $M(1)_a$, of central charge $1-12a^2$. We classify these operators in terms of {\em depth} and provide explicit constructions in all cases. Furthermore, for $a=0$ we focus on the vertex operator subalgebra L(1,0) of $M(1)_0$ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of {\em hidden} logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1,0)-module.Comment: 32 pages. To appear in CM

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

The N=1 triplet vertex operator superalgebras

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We classify irreducible SW(m)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible SW(m) characters. Finally, we contemplate possible connections between the category of SW(m)-modules and the category of modules for the quantum group U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)). This paper is a continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version, to appear in CM

The Bloch-Okounkov correlation functions of classical type

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable gl_\infty-modules of level one. Such gl_\infty-correlation functions at higher levels were then calculated by Cheng and Wang. In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of gl_\infty of type B,C,D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B,C,D and some fermionic type q-identities.Comment: v2, very minor changes, Latex, 41 pages, to appear in Commun. Math. Phy

The logarithmic triplet theory with boundary

The boundary theory for the c=-2 triplet model is investigated in detail. In particular, we show that there are four different boundary conditions that preserve the triplet algebra, and check the consistency of the corresponding boundary operators by constructing their OPE coefficients explicitly. We also compute the correlation functions of two bulk fields in the presence of a boundary, and verify that they are consistent with factorisation.Comment: 43 pages, LaTeX; v2: references added, typos corrected, footnote 4 adde

From boundary to bulk in logarithmic CFT

The analogue of the charge-conjugation modular invariant for rational logarithmic conformal field theories is constructed. This is done by reconstructing the bulk spectrum from a simple boundary condition (the analogue of the Cardy `identity brane'). We apply the general method to the c_1,p triplet models and reproduce the previously known bulk theory for p=2 at c=-2. For general p we verify that the resulting partition functions are modular invariant. We also construct the complete set of 2p boundary states, and confirm that the identity brane from which we started indeed exists. As a by-product we obtain a logarithmic version of the Verlinde formula for the c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in J.Phys.

Viscoelastic gels of guar and xanthan gum mixtures provide long-term stabilization of iron micro- and nanoparticles

Iron micro- and nanoparticles used for groundwater remediation and medical applications are prone to fast aggregation and sedimentation. Diluted single biopolymer water solutions of guar gum (GG) or xanthan gum (XG) can stabilize these particles for few hours providing steric repulsion and by increasing the viscosity of the suspension. The goal of the study is to demonstrate that amending GG solutions with small amounts of XG (XG/GG weight ratio 1:19; 3 g/L of total biopolymer concentration) can significantly improve the capability of the biopolymer to stabilize highly concentrated iron micro- and nanoparticle suspensions. The synergistic effect between GG and XG generates a viscoelastic gel that can maintain 20 g/L iron particles suspended for over 24 h. This is attributed to (i) an increase in the static viscosity, (ii) a combined polymer structure the yield stress of which contrasts the downward stress exerted by the iron particles, and (iii) the adsorption of the polymers to the iron surface having an anchoring effect on the particles. The XG/GG viscoelastic gel is characterized by a marked shear thinning behavior. This property, coupled with the low biopolymer concentration, determines small viscosity values at high shear rates, facilitating the injection in porous media. Furthermore, the thermosensitivity of the soft elastic polymeric network promotes higher stability and longer storage times at low temperatures and rapid decrease of viscosity at higher temperatures. This feature can be exploited in order to improve the flowability and the delivery of the suspensions to the target as well as to effectively tune and control the release of the iron particle

Mechanisms for Tuning Engineered Nanomaterials to Enhance Radiation Therapy of Cancer.

Engineered nanomaterials that produce reactive oxygen species on exposure to X- and gamma-rays used in radiation therapy offer promise of novel cancer treatment strategies. Similar to photodynamic therapy but suitable for large and deep tumors, this new approach where nanomaterials acting as sensitizing agents are combined with clinical radiation can be effective at well-tolerated low radiation doses. Suitably engineered nanomaterials can enhance cancer radiotherapy by increasing the tumor selectivity and decreasing side effects. Additionally, the nanomaterial platform offers therapeutically valuable functionalities, including molecular targeting, drug/gene delivery, and adaptive responses to trigger drug release. The potential of such nanomaterials to be combined with radiotherapy is widely recognized. In order for further breakthroughs to be made, and to facilitate clinical translation, the applicable principles and fundamentals should be articulated. This review focuses on mechanisms underpinning rational nanomaterial design to enhance radiation therapy, the understanding of which will enable novel ways to optimize its therapeutic efficacy. A roadmap for designing nanomaterials with optimized anticancer performance is also shown and the potential clinical significance and future translation are discussed

Serum nucleosomes during neoadjuvant chemotherapy in patients with cervical cancer. Predictive and prognostic significance

BACKGROUND: It has been shown that free DNA circulates in serum plasma of patients with cancer and that at least part is present in the form of oligo- and monucleosomes, a marker of cell death. Preliminary data has shown a good correlation between decrease of nucleosomes with response and prognosis. Here, we performed pre- and post-chemotherapy determinations of serum nucleosomes with an enzyme-linked immunosorbent assay (ELISA) method in a group of patients with cervical cancer receiving neoadjuvant chemotherapy. METHODS: From December 2000 to June 2001, 41 patients with cervical cancer staged as FIGO stages IB2-IIIB received three 21-day courses of carboplatin and paclitaxel, both administered at day 1; then, patients underwent radical hysterectomy. Nucleosomes were measured the day before (baseline), at day seven of the first course and day seven of the third course of chemotherapy. Values of nucleosomes were analyzed with regard to pathologic response and to time to progression-free and overall survival. RESULTS: All patients completed chemotherapy, were evaluable for pathologic response, and had nucleosome levels determined. At a mean follow-up of 23 months (range, 7–26 months), projected progression time and overall survival were 80.3 and 80.4%, respectively. Mean differential values of nucleosomes were lower in the third course as compared with the first course (p >0.001). The decrease in the third course correlated with pathologic response (p = 0.041). Survival analysis showed a statistically significant, better progression-free and survival time in patients who showed lower levels at the third course (p = 0.0243 and p = 0.0260, respectively). Cox regression analysis demonstrated that nucleosome increase in the third course increased risk of death to 6.86 (95% confidence interval [CI 95%], 0.84–56.0). CONCLUSION: Serum nucleosomes may have a predictive role for response and prognostic significance in patients with cervical cancer patients treated with neoadjuvant chemotherapy