Topological Sectors and Measures on Moduli Space in Quantum Yang-Mills on a Riemann Surface

Previous path integral treatments of Yang-Mills on a Riemann surface automatically sum over principal fiber bundles of all possible topological types in computing quantum expectations. This paper extends the path integral formulation to treat separately each topological sector. The formulation is sufficiently explicit to calculate Wilson line expectations exactly. Further, it suggests two new measures on the moduli space of flat connections, one of which proves to agree with the small-volume limit of the Yang-Mills measure. \copyright {\em 1996 American Institute of Physics.}Comment: 13 pages, Latex (v. 2.09), figure available on request, revised to add 2 new references, clarify exposition, fix typos. Version to appear in J. Math. Phys., Spring 199

Energy in Yang-Mills on a Riemann Surface

Sengupta's lower bound for the Yang-Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The Yang-Mills critical sets correspond to critical sets of the energy action on a space of paths. This may shed light on Atiyah and Bott's conjecture concerning Morse theory for the space of connections modulo gauge transformations.Comment: 7 pages, 2 figures, Latex2e with epsfig, submitted to Journal of Mathematical Physic

A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel

In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of piecewise geodesic paths, the kernel of the time evolution operator is the heat kernel for the Laplacian on forms. The path integral is approximated by the integral of a form on the space of piecewise geodesic paths which is the pullback by a natural section of Mathai and Quillen's Thom form of a bundle over this space. In the case of closed paths, the bundle is the tangent space to the space of geodesic paths, and the integral of this form passes in the limit to the supertrace of the heat kernel.Comment: 14 pages, LaTeX, no fig

The Use of Rodent Models to Investigate Host-Bacteria Interactions Related to Periodontal Diseases

Even though animal models have limitations they are often superior to in vitro or clinical studies in addressing mechanistic questions and serve as an essential link between hypotheses and human patients. Periodontal disease can be viewed as a process that involves four major stages: bacterial colonization, invasion, induction of a destructive host response in connective tissue and a repair process that reduces the extent of tissue breakdown. Animal studies should be evaluated in terms of their capacity to test specific hypotheses rather than their fidelity to all aspects of periodontal disease initiation and progression. Thus, each of the models described below can be adapted to test discrete components of these four major steps, but not all of them. This review describes five different animal models that are appropriate for examining components of host-bacteria interactions that can lead to breakdown of hard and soft connective tissue or conditions that limit its repair as follows: the mouse calvarial model, murine oral gavage models with or without adoptive transfer of human lymphocytes, rat ligature model and rat Aggregatibacter actinomycetemcomitans feeding model

Bacterial Infection Increases Periodontal Bone Loss in Diabetic Rats Through Enhanced Apoptosis

Periodontal disease is the most common osteolytic disease in humans and is significantly increased by diabetes mellitus. We tested the hypothesis that bacterial infection induces bone loss in diabetic animals through a mechanism that involves enhanced apoptosis. Type II diabetic rats were inoculated with Aggregatibacter actinomycetemcomitans and treated with a caspase-3 inhibitor, ZDEVD-FMK, or vehicle alone. Apoptotic cells were measured with TUNEL; osteoblasts and bone area were measured in H&E sections. New bone formation was assessed by labeling with fluorescent dyes and by osteocalcin mRNA levels. Osteoclast number, eroded bone surface, and new bone formation were measured by tartrate-resistant acid phosphatase staining. Immunohistochemistry was performed with an antibody against tumor necrosis factor-α. Bacterial infection doubled the number of tumor necrosis factor-α–expressing cells and increased apoptotic cells adjacent to bone 10-fold (P \u3c 0.05). Treatment with caspase inhibitor blocked apoptosis, increased the number of osteoclasts, and eroded bone surface (P \u3c 0.05); yet, inhibition of apoptosis resulted in significantly greater net bone area because of an increase in new bone formation, osteoblast numbers, and an increase in bone coupling. Thus, bacterial infection in diabetic rats stimulates periodontitis, in part through enhanced apoptosis of osteoblastic cells that reduces osseous coupling through a caspase-3–dependent mechanism. Diabetes is a chronic inflammatory disease characterized by hyperglycemia that affects 26 million Americans.1 Diabetes has several complications, such as cardiovascular, renal, microvascular, and periodontal diseases. Periodontal disease is one of the most common forms of osteolytic bone disease and one of the most frequent complications of the diabetes.2 Recent research suggests that the relationship between periodontitis and diabetes is reciprocal.3, 4 People with diabetes are more susceptible to periodontitis, and periodontitis may affect serum glucose levels and contribute to progression of diabetes.5 Diabetes may contribute to periodontitis because of its effect on inflammation.6, 7 Despite being triggered by bacterial infection, periodontal bone loss is tied to the inflammatory host response, which leads to the generation of prostaglandins and cytokines that stimulate osteoclastogenesis and periodontal bone loss.8 Several of the detrimental aspects of periodontal disease have recently been shown to be mediated by elevated levels of tumor necrosis factor-α (TNF-α).9, 10 TNF-α is a proinflammatory cytokine produced by leukocytes and other cell types.11 Enhanced TNF-α levels have been directly linked to cellular changes in diabetic retinopathy, deficits in wound healing, and diabetes-enhanced periodontitis.12, 13, 14 Some of the detrimental effects of diabetes-enhanced TNF-α levels may be because of the induction of cell death by triggering caspase activity. Caspases are a family of cysteine proteases that can act as either initiators (caspases 2, 8, and 9) or executioners (caspases 3, 6, and 7) of apoptosis.15 Caspase-3 appears to play a central role in bacteria and lipopolysaccharide-mediated apoptosis.16, 17 In addition, it has been shown that TNF-α can stimulate the expression of several pro-apoptotic genes, many of which are regulated by the pro-apoptotic transcription factor, forkhead box-O1 (FOXO1).18 The functional role of apoptosis in pathological processes can be studied with caspase inhibitors, which are small peptides that block the activity of well-defined caspases.19 These inhibitors have been used in animal models to attenuate cell death and diminish tissue damage in ischemic conditions, sepsis, and other pathological processes.20, 21 Other studies using caspase inhibitors have shown that part of the detrimental effect of diabetes on healing after infection is the result of increased fibroblast or osteoblast apoptosis.16, 22 To understand how diabetes may affect periodontal bone loss through apoptosis, we used a caspase-3/7 inhibitor in a type 2 Goto-Kakizaki (GK) diabetic rat model of periodontal disease induced by bacterial infection. The aim of this study was to determine how apoptosis of osteoblasts contributed to periodontal bone loss by its effect on bone formation in diabetic animals

A.Actinomycetemcomitans‐Induced Periodontal Disease Promotes Systemic and Local Responses in Rat Periodontium

Aim To characterize the histologic and cellular response to A. actinomycetemcomitans (Aa) infection. Material & Methods Wistar rats infected with Aa were evaluated for antibody response, oral Aa colonization, loss of attachment, PMN recruitment, TNF‐α in the junctional epithelium and connective tissue, osteoclasts and adaptive immune response in local lymph nodes at baseline and 4, 5 or 6 weeks after infection. Some groups were given antibacterial treatment at 4 weeks. Results An antibody response against Aa occurred within 4 weeks of infection, and 78% of inoculated rats had detectable Aa in the oral cavity (p \u3c 0.05). Aa infection significantly increased loss of attachment that was reversed by antibacterial treatment (p \u3c 0.05). TNF‐α expression in the junctional epithelium followed the same pattern. Aa stimulated high osteoclast formation and TNF‐α expression in the connective tissue (p \u3c 0.05). PMN recruitment significantly increased after Aa infection (p \u3c 0.05). Aa also increased the number of CD8+ T cells (p \u3c 0.05), but not CD4+ T cells or regulatory T cells (Tregs) (p \u3e 0.05). Conclusion Aa infection stimulated a local response that increased numbers of PMNs and TNF‐α expression in the junctional epithelium and loss of attachment. Both TNF‐α expression in JE and loss of attachment was reversed by antibiotic treatment. Aa infection also increased TNF‐α in the connective tissue, osteoclast numbers and CD8+ T cells in lymph nodes. The results link Aa infection with important characteristics of periodontal destruction

Surveillance for Anthrax Cases Associated with Contaminated Letters, New Jersey, Delaware, and Pennsylvania, 2001

In October 2001, two inhalational anthrax and four cutaneous anthrax cases, resulting from the processing of Bacillus anthracis–containing envelopes at a New Jersey mail facility, were identified. Subsequently, we initiated stimulated passive hospital-based and enhanced passive surveillance for anthrax-compatible syndromes. From October 24 to December 17, 2001, hospitals reported 240,160 visits and 7,109 intensive-care unit admissions in the surveillance area (population 6.7 million persons). Following a change to reporting criteria on November 8, the average of possible inhalational anthrax reports decreased 83% from 18 to 3 per day; the proportion of reports requiring follow-up increased from 37% (105/286) to 41% (47/116). Clinical follow-up was conducted on 214 of 464 possible inhalational anthrax patients and 98 possible cutaneous anthrax patients; 49 had additional laboratory testing. No additional cases were identified. To verify the limited scope of the outbreak, surveillance was essential, though labor-intensive. The flexibility of the system allowed interim evaluation, thus improving surveillance efficiency