System of Complex Brownian Motions Associated with the O'Connell Process

The O'Connell process is a softened version (a geometric lifting with a parameter $a>0$) of the noncolliding Brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length $a$. This process is not determinantal. Under a special entrance law, however, Borodin and Corwin gave a Fredholm determinant expression for the expectation of an observable, which is a softening of an indicator of a particle position. We rewrite their integral kernel to a form similar to the correlation kernels of determinantal processes and show, if the number of particles is $N$, the rank of the matrix of the Fredholm determinant is $N$. Then we give a representation for the quantity by using an $N$-particle system of complex Brownian motions (CBMs). The complex function, which gives the determinantal expression to the weight of CBM paths, is not entire, but in the combinatorial limit $a \to 0$ it becomes an entire function providing conformal martingales and the CBM representation for the noncolliding Brownian motion is recovered.Comment: v3: AMS_LaTeX, 25 pages, no figure, minor corrections made for publication in J. Stat. Phy

Diagnostic Criteria of Ulcerative Pyoderma Gangrenosum : A Delphi Consensus of International Experts

IMPORTANCE Pyoderma gangrenosum is a rare inflammatory skin condition that is difficult to diagnose. Currently, it is a "diagnosis of exclusion," a definition not compatible with clinical decision making or inclusion for clinical trials. OBJECTIVE To propose and validate diagnostic criteria for ulcerative pyoderma gangrenosum. EVIDENCE REVIEW Diagnostic criteria were created following a Delphi consensus exercise using the RAND/UCLA Appropriateness Method. The criteria were validated against peer-reviewed established cases of pyoderma gangrenosum and mimickers using k-fold cross-validation with methods of multiple imputation. FINDINGS Delphi exercise yielded 1 major criterion biopsy of ulcer edge demonstrating neutrophilic infiltrate and 8 minor criteria: (1) exclusion of infection; (2) pathergy; (3) history of inflammatory bowel disease or inflammatory arthritis; (4) history of papule, pustule, or vesicle ulcerating within 4 days of appearing; (5) peripheral erythema, undermining border, and tenderness at ulceration site; (6) multiple ulcerations, at least 1 on an anterior lower leg; (7) cribriform or "wrinkled paper" scar(s) at healed ulcer sites; and (8) decreased ulcer size within 1 month of initiating immunosuppressive medication(s). Receiver operating characteristic analysis revealed that 4 of 8 minor criteria maximized discrimination, yielding sensitivity and specificity of 86% and 90%, respectively. CONCLUSIONS AND RELEVANCE. This Delphi exercise produced 1 major criterion and 8 minor criteria for the diagnosis of ulcerative pyoderma gangrenosum. The criteria may serve as a guideline for clinicians, allowing for fewer misdiagnoses and improved patient selection for clinical trials

T-cell regulation in Erythema Nodosum Leprosum.

Leprosy is a disease caused by Mycobacterium leprae where the clinical spectrum correlates with the patient immune response. Erythema Nodosum Leprosum (ENL) is an immune-mediated inflammatory complication, which causes significant morbidity in affected leprosy patients. The underlying cause of ENL is not conclusively known. However, immune-complexes and cell-mediated immunity have been suggested in the pathogenesis of ENL. The aim of this study was to investigate the regulatory T-cells in patients with ENL. Forty-six untreated patients with ENL and 31 non-reactional lepromatous leprosy (LL) patient controls visiting ALERT Hospital, Ethiopia were enrolled to the study. Blood samples were obtained before, during and after prednisolone treatment of ENL cases. Peripheral blood mononuclear cells (PBMCs) were isolated and used for immunophenotyping of regulatory T-cells by flow cytometry. Five markers: CD3, CD4 or CD8, CD25, CD27 and FoxP3 were used to define CD4+ and CD8+ regulatory T-cells. Clinical and histopathological data were obtained as supplementary information. All patients had been followed for 28 weeks. Patients with ENL reactions had a lower percentage of CD4+ regulatory T-cells (1.7%) than LL patient controls (3.8%) at diagnosis of ENL before treatment. After treatment, the percentage of CD4+regulatory T-cells was not significantly different between the two groups. The percentage of CD8+ regulatory T-cells was not significantly different in ENL and LL controls before and after treatment. Furthermore, patients with ENL had higher percentage of CD4+ T-ells and CD4+/CD8+ T-cells ratio than LL patient controls before treatment. The expression of CD25 on CD4+ and CD8+ T-cells was not significantly different in ENL and LL controls suggesting that CD25 expression is not associated with ENL reactions while FoxP3 expression on CD4+ T-cells was significantly lower in patients with ENL than in LL controls. We also found that prednisolone treatment of patients with ENL reactions suppresses CD4+ T-cell but not CD8+ T-cell frequencies. Hence, ENL is associated with lower levels of T regulatory cells and higher CD4+/CD8+ T-cell ratio. We suggest that this loss of regulation is one of the causes of ENL