Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow

We prove that solutions of a mildly regularized Perona-Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the general principle that "the limit of gradient-flows is the gradient-flow of the limit". To this end, we exploit a general result relating the Gamma-limit of a sequence of functionals to the limit of the corresponding maximal slope curves.Comment: 19 page

Slow time behavior of the semidiscrete Perona-Malik scheme in dimension one

We consider the long time behavior of the semidiscrete scheme for the Perona-Malik equation in dimension one. We prove that approximated solutions converge, in a slow time scale, to solutions of a limit problem. This limit problem evolves piecewise constant functions by moving their plateaus in the vertical direction according to a system of ordinary differential equations. Our convergence result is global-in-time, and this forces us to face the collision of plateaus when the system singularizes. The proof is based on energy estimates and gradient-flow techniques, according to the general idea that "the limit of the gradient-flows is the gradient-flow of the limit functional". Our main innovations are a uniform H\"{o}lder estimate up to the first collision time included, a well preparation result with a careful analysis of what happens at discrete level during collisions, and renormalizing the functionals after each collision in order to have a nontrivial Gamma-limit for all times.Comment: 42 page

Goodbye from Milan!

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diagnosis of liver nodules within and outside screening programs

Evaluation of a liver nodule detected with ultrasound includes the recovery of a detailed medical history, a physical exam, appropriate contrast imaging examinations and, in selected cases, histopathology. In this setting, identification of liver disease accompanying a liver nodule helps distinction between benign nodules and metastatic malignant nodules from primary liver cancer, as recommended by scientific liver societies. Diagnostic algorithms for a liver nodule in patients with liver disease involve contrast CT scan, magnetic resonance imaging or contrast enhanced ultrasounds to show the typical neoplastic pattern of early arterial hyperenhancement wash-in followed by hypoenhancement in the late portal phase wash out. The flow charts developed by western societies utilize the discriminant criterion of tumor size i.e. the radiological diagnosis being endorsed in a nodule equal or greater than 1 cm whereas eastern societies rely on the recognition of a typical vascular pattern of the node, independently of size. Differential diagnosis should be obtained to differentiate liver related nodules like regenerative macronodules (more than 20% of the cases) and the less frequent intrahepatic cholangiocarcinoma (~2% of the cases) from liver disease unrelated nodules like hemangioma (~4%), neuroendocrine metastatic nodules (~1%) and focal nodular hyperplasia. In patients without liver disease, the most common liver nodules in the liver are hemangioma (~1.5%), focal nodular hyperplasia (0.03%) and hepatocellular adenoma (up to 0.004% in long term users of oral contraceptives). Optimization of management of patients with a liver nodule requires establishment of a multidisciplinary clinic

Fiscal Federalism and Endogenous Lobbies' Formation

We study lobbying behavior by firms in a two-region economy, with either centralized or decentralized provision of profit-enhancing local public goods. Firms compete either in the market, lobbying for public good provision once entered in a market, or for the market, lobbying to gain ccess to it. When firms compete in the market, we show that lobbying is unambiguously less disruptive or social welfare under decentralization. Moreover, foreign rather than domestic private nterests may be more powerful in a.ecting regional policies. On the contrary, when firms compete or the market, lobbying is mostly e.ective under decentralization, since local firms always end p forming a local monopoly. However, we show that an institutional setting in which competencies re split between the center and the periphery may dominate either full centralization or full ecentralization or both.fiscal federalism, lobbying, private interests

Impact of M&A on the R&D process. An empirical analysis of the role of technological and market relatedness, The

While the impact of M&A on R&D and innovation examined at the aggregate level left inconclusive evidence, we find that at the level of the R&D process both the technological and the market relatedness between the target and the acquirer are helpful dimensions to identify effects. Using information on 31 in-depth cases of individual M&A deals we show that technological relatedness between M&A partners directly affects the inputs and organizational structure of the R&D process. M&A partners that operate in the same technological fields tend to reduce their R&D effort and rationalize the R&D process after the M&A compared to firms active in complementary technological fields that merge. These firms will furthermore face less technological competition in the technology market, but risk creating a more bureaucratic R&D process with a less motivated workforce. Market relatedness between partners, while having comparable aggregate effects on the R&D process, operates on different dimensions of the R&D process. Former rivals that engage in a M&A are significantly less likely to expand into new R&D fields or leverage their technological competences across the products and markets of the new entity. Non-rival firms that join forces, in contrast, significantly increase R&D output and productivity through these activities.M&A; R&D; scale and scope; market relatedness; technological relatedness;

Ground state and excitation dynamics in Ag doped helium clusters

We present a quantum Monte Carlo study of the structure and energetics of silver doped helium clusters AgHe$_n$ for $n$ up to 100. Our simulations show the first solvation shell of the Ag atom to be composed by roughly 20 He atoms, and to possess a structured angular distribution. Moreover, the electronic $^2$P$_{1/2}\leftarrow ^2$S$_{1/2}$ and $^2$P$_{3/2}\leftarrow ^2$S$_{1/2}$ electronic transitions of the embedded silver impurity have been studied as a function of the number ofhelium atoms. The computed spectra show a redshift for $n\leq 15$ and an increasing blueshift for larger clusters, a feature attributed to the effect of the second solvation shell of He atoms. For the largest cluster, the computed excitation spectrum is found in excellent agreement with the ones recorded in superfluid He clusters and bulk. No signature of the direct formation of proposed AgHe$_2$ exciplex is present in the computed spectra of AgHe$_{100}$.Comment: 4 Pages, 3 Figures, submitted to Phys. Rev. Let

Peginterferon maintenance therapy in patients with advanced hepatitis C to prevent hepatocellular carcinoma: The plot thickens

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Genetic testing for hepatocellular carcinoma: An ambitious goal still to achieve

Background & Aims: A single nucleotide polymorphism 61⁄G (rs4444903) in the epidermal growth factor (EGF) gene has been associated, in two case–control studies, with hepatocellular carcinoma (HCC). We tested associations between demographic, clinical, and genetic data and development of HCC, and developed a simple predictive model in a cohort of patients with chronic hepatitis C and advanced fibrosis. Methods: Black and white subjects from the Hepatitis C Antiviral Long-term Treatment against Cirrhosis (HALT-C) trial (n = 816) were followed up prospectively for development of a definite or presumed case of HCC for a median time period of 6.1 years. We used the Cox proportional hazards regression model to determine the hazard ratio for risk of HCC and to develop prediction models. Results: Subjects with EGF genotype G/G had a higher adjusted risk for HCC than those with genotype A/A (hazard ratio, 2.10; 95% confidence interval, 1.05–4.23; P = .03). After adjusting for EGF genotype, blacks had no increased risk of HCC risk compared with whites. Higher serum levels of EGF were observed among subjects with at least one G allele (P = .08); the subset of subjects with EGF G/G genotype and above-median serum levels of EGF had the highest risk of HCC. We developed a simple prediction model that included the EGF genotype to identify patients at low, intermediate, and high risk for HCC; 6-year cumulative HCC incidences were 2.3%, 10.4%, and 26%, respectively. Conclusions: We associated the EGF genotype G/G with increased risk for HCC; differences in its frequency among black and white subjects might account for differences in HCC incidence between these Journal of Hepatology 2

Fiscal Federalism and Endogenous Lobbies' Formation

We study lobbying behavior by firms in a two-region economy, with either centralized or decentralized provision of profit-enhancing local public goods. Firms compete either in the market, lobbying for public good provision once entered in a market, or for the market, lobbying to gain ccess to it. When firms compete in the market, we show that lobbying is unambiguously less disruptive or social welfare under decentralization. Moreover, foreign rather than domestic private nterests may be more powerful in a.ecting regional policies. On the contrary, when firms compete or the market, lobbying is mostly e.ective under decentralization, since local firms always end p forming a local monopoly. However, we show that an institutional setting in which competencies re split between the center and the periphery may dominate either full centralization or full ecentralization or both