Privately optimal severance pay

This paper constructs an equilibrium matching model with risk-averse workers and incomplete contracts to study both the optimal private provision of severance pay and the consequences of government mandates in excess of the private optimum. The privately-optimal severance payment is bounded below by the fall in lifetime wealth resulting from job loss. Despite market incompleteness, mandated minimum payments significantly exceeding the private optimum are effectively undone by adjustment of the contractual wage, and have only small allocational and welfare effects

Matrix models for stationary Gromov-Witten invariants of the Riemann sphere

Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of $\mathbb{P}^1$ as an isomonodromic tau function associated with a difference equation. As a byproduct we obtain an analogue of the Kontsevich matrix model for this tau function. A connection with the Charlier ensemble is also considered.Comment: v3: new appendix

Long-Term Outcome of Rectal Cancer With Clinically (EUS/MRI) Metastatic Mesorectal Lymph Nodes Treated by Neoadjuvant Chemoradiation: Role of Organ Preservation Strategies in Relation to Pathologic Response

Organ preservation strategies are under investigation for patients with locally advanced rectal cancer (LARC) who achieve a complete pathologic response in the primary tumor (ypT0) after neoadjuvant chemoradiation therapy (CRT). This study explored the value of this approach for cN+ patients.Data were retrieved from our institutional prospective rectal cancer database. Tumors with mesorectal lymph nodes larger than 5 mm shown on endorectal ultrasonography, pelvic magnetic resonance imaging, or both were staged as cN+.The study population comprised 226 patients (142 men and 84 women; median age, 64 years) with LARC who underwent CRT followed by surgery including total mesorectal excision (TME) (n = 179) and full-thickness local excision (LE) (n = 47) between 1996 and 2013. At staging, 123 patients (54.4 %) were cN+. In 65 cases (28.7 %), ypCR was observed. Metastatic mesorectal lymph nodes (ypN+) were detected in 41.6 % of the cN+ patients and in 2.8 % of the cN0 patients (P < 0.01). Among the cN+ patients, 16 % of the ypT0 cases were ypN+ compared with 51.8 % of the no-ypT0 cases (P < 0.01). Among the cN+ patients who underwent TME, the 5-year disease-specific survival (DSS) and disease-free survival (DFS) rates were respectively 100 and 91.6 % for the ypT0 patients compared with 71.2 and 58.0 % for the no-ypT0 patients (P = 0.01). Among the ypN+ patients, the 5-year DSS and DFS rates were both 100 % for the ypT0 cases compared with 59.1 and 43.3 % for the no-ypT0 patients. Among the cN+ and ypT0 patients, the 5-year DSS and DFS were respectively 100 and 85.7 % for the TME patients compared with 100 and 91.6 % for the LE patients. In the multivariate analysis, ypT0 was the only independent prognostic factor.Protocols aimed at organ preservation in LARC that achieve ypT0 after CRT can be offered also to cN+ patients

The Kontsevich\u2013Penner Matrix Integral, Isomonodromic Tau Functions and Open Intersection Numbers.

We identify the Kontsevich\u2013Penner matrix integral, for finite size n, with the isomonodromic tau function of a 3 73 rational connection on the Riemann sphere with n Fuchsian singularities placed in correspondence with the eigenvalues of the external field of the matrix integral. By formulating the isomonodromic system in terms of an appropriate Riemann\u2013Hilbert boundary value problem, we can pass to the limit \u2192 1e (at a formal level) and identify an isomonodromic system in terms of Miwa variables, which play the role of times of a KP hierarchy. This allows to derive the String and Dilaton equations via a purely Riemann\u2013Hilbert approach. The expression of the formal limit of the partition function as an isomonodromic tau function allows us to derive explicit closed formul\ue6 for the correlators of this matrix model in terms of the solution of the Riemann Hilbert problem with all times set to zero. These correlators have been conjectured to describe the intersection numbers for Riemann surfaces with boundaries, or open intersection numbers