On the Product Knapsack Problem

Given a set of items, each characterized by a profit and a weight, we study the problem of maximizing the product of the profits of the selected items, while respecting a given capacity. To the best of our knowledge this is the first manuscript that studies this variant of the knapsack problem which we call Product Knapsack Problem (PKP). We show that PKP is weakly NP-hard. We propose and implement a Dynamic Programming algorithm and different Mixed Integer Linear and Nonlinear Programming formulations for the PKP. Finally, we present an extensive computational study on a large set of benchmark instances derived from the literature

Matematica, stupore e poesia

Questo libro vuole dimostrare che la matematica, lungi dall'essere disciplina fredda e austera, \ue8 invece umanesimo tra gli umanesimi, vera fonte culturale di riflessioni profonde, proprio come la poesia, le arti, e le lettere. Il volume \ue8 strutturato in nove capitoli e tratta con un registro le varie problematiche che sono connesse tra matematica e arte: che cos'\ue8 veramente la matematica? Qual'\ue8 il suo linguaggio? Esiste un legame tra matematica e poesia? Con contributi di Piergiorgio Odifreddi, Michele Emmer e Gabriele Lolli, questo libro racconta di una disciplina che troppo spesso \ue8 percepita fine a se stessa

Polymyxin-B hemoperfusion in septic patients: analysis of a multicenter registry

Background: In 2010, the EUPHAS 2 collaborative group created a registry with the purpose of recording data from critically ill patients suffering from severe sepsis and septic shock treated with polymyxin-B hemoperfusion (PMX-HP) for endotoxin removal. The aim of the registry was to verify the application of PMX-HP in the daily clinical practice. Methods: The EUPHAS 2 registry involved 57 centers between January 2010 and December 2014, collecting retrospective data of 357 patients (297 in Europe and 60 in Asia) suffering from severe sepsis and septic shock caused by proved or suspected infection related to Gram negative bacteria. All patients received atleast one cycle of extracorporeal endotoxin removal by PMX-HP. Results: Septic shock was diagnosed in 305 (85.4 %) patients. The most common source of infection was abdominal (44.0 %) followed by pulmonary (17.6 %). Gram negative bacteria represented 60.6 % of the pathogens responsible of infection. After 72 h from the first cycle of PMX-HP, some of the SOFA score components significantly improved with respect to baseline: cardiovascular (2.16 \ub1 1.77 from 3.32 \ub1 1.29, p < 0.0001), respiratory (1.95 \ub1 0.95 from 2.40 \ub1 1.06, p < 0.001) and renal (1.84 \ub1 1.77 from 2.23 \ub1 1.62, p = 0.013). Overall 28-day survival rate was 54.5 % (60.4 % in abdominal and 47.5 % in pulmonary infection). Patients with abdominal infection treated with PMX-HP within 24 h from the diagnosis of septic shock had a 28-day survival rate of 64.5 %. Patients showing a significantly cardiovascular improvement after PMX-HP had a 28-survival rate of 75 % in comparison to the 39 % of patients who did not (p < 0.001). Cox regression analysis found the variation of cardiovascular, respiratory and coagulation SOFA to be independent covariates for 28-day survival. In European patients were observed a higher 28-day (58.8 vs. 34.5 %, p = 0.003), ICU (59 vs. 36.7 %, p = 0.006) and hospital survival rate (53.2 vs. 35 %, p = 0.02) than in Asian patients. However, the two populations were highly heterogeneous in terms of source of infection and severity scores at admission. Conclusion: The EUPHAS 2 is the largest registry conducted outside Japan on the clinical use of PMX-HP in septic patients. Data analysis confirmed the feasibility of PMX-HP to treat septic patients in daily clinical practice, showing clinical benefits associated with endotoxin removal without significant adverse events related to the extracorporeal technique