The density and complexity of polynomial cores for intractable sets

Let A be a recursive problem not in P. Lynch has shown that A then has an infinite recursive polynomial complexity core. This is a collection C of instances of A such that every algorithm deciding A needs more than polynomial time almost everywhere on C. We investigate the complexity of recognizing the instances in such a core, and show that every recursive problem A not in P has an infinite core recognizable in subexponential time. We further study how dense the core sets for A can be, under various assumptions about the structure of A. Our main results in this direction are that if P ≠ NP, then NP-complete problems have polynomially nonsparse cores recognizable in subexponential time, and that EXPTIME-complete problems have cores of exponential density recognizable in exponential time

Turing machines with few accepting computations and low sets for PP

Peer Reviewe

On bounded query machines

AbstractSimple proofs are given for each of the following results: (a) P = Pspace if and only if, for every set A, P(A) = Pquery(A) (Selman et al., 1983): (b) NP = Pspace if and only if, for every set A, NP(A) = NPquery(S) (Book, 1981); (c) PH = Pspace if and only if, for every set A, PH(A) = PQH(A) (Book and Wrathall, 1981); (c) PH = Pspace if and only if, for every set set S, PH(S) = PQH(S) = Pspace(S) (Balcázar et al., 1986; Long and Selman, 1986)

Instance Complexity

Peer reviewe

Treatment of Intrahepatic Cholangiocarcinoma—A Multidisciplinary Approach

Intrahepatic cholangiocarcinoma (iCC) is distinguished as an entity from perihilar and distal cholangiocarcinoma and gallbladder carcinoma. Recently, molecular profiling and histopathological features have allowed further classification. Due to the frequent delay in diagnosis, the prognosis for iCC remains poor despite major technical advances and multimodal therapeutic approaches. Liver resection represents the therapeutic backbone and only curative treatment option, with the functional residual capacity of the liver and oncologic radicality being deciding factors for postoperative and long-term oncological outcome. Furthermore, in selected cases and depending on national guidelines, liver transplantation may be a therapeutic option. Given the often advanced tumor stage at diagnosis or the potential for postoperative recurrence, locoregional therapies have become increasingly important. These strategies range from radiofrequency ablation to transarterial chemoembolization to selective internal radiation therapy and can be used in combination with liver resection. In addition, adjuvant and neoadjuvant chemotherapies as well as targeted therapies and immunotherapies based on molecular profiles can be applied. This review discusses multimodal treatment strategies for iCC and their differential use

A tailored approach in lymph node-positive perihilar cholangiocarcinoma

Purpose Extended right hepatectomy is associated with wide surgical margins in PHC and often favored for oncological considerations. However, it remains uncertain whether established surgical principles also apply to the subgroup of node-positive patients. The aim of the present study was to define a tailored surgical approach for patients with perihilar cholangiocarcinoma (PHC) and lymph node metastases. Methods We reviewed the course of all consecutive patients undergoing major hepatectomy for PHC between 2005 and 2015 at the Department of Surgery, Charite - Universitatsmedizin Berlin. Results Two hundred and thirty-one patients underwent major hepatectomy for PHC with 1-, 3-, and 5-year overall (OS) and disease-free survival (DFS) rates of 72%, 48%, and 36%, and 60%, 22%, and 12%, respectively. In lymph node-positive patients (n = 109, 47%), extended left hepatectomy was associated with improved OS and DFS, respectively, when compared to extended right hepatectomy (p = 0.008 and p = 0.003). Interestingly, OS and DFS did not differ between R0 and R1 resections in those patients (both p = ns). Patients undergoing extended left hepatectomy were more likely to receive adjuvant chemotherapy (p = 0.022). This is of note as adjuvant chemotherapy, besides grading (p = 0.041), was the only independent prognostic factor in node-positive patients (p=0.002). Conclusion Patients with node-positive PHC might benefit from less aggressive approaches being associated with lower morbidity and a higher chance for adjuvant chemotherapy. Lymph node sampling might help to guide patients to the appropriate surgical approach according to their lymph node status

Hospitalization Before Liver Transplantation Predicts Posttransplant Patient Survival: A Propensity Score–Matched Analysis

In contrast to donor factors predicting outcomes of liver transplantation (LT), few suitable recipient parameters have been identified. To this end, we performed an in-depth analysis of hospitalization status and duration prior to LT as a potential risk factor for posttransplant outcome. The pretransplant hospitalization status of all patients undergoing LT between 2005 and 2016 at the Charité-Universitätsmedizin Berlin was analyzed retrospectively using propensity score matching. At the time of organ acceptance, 226 of 1134 (19.9%) recipients were hospitalized in an intensive care unit (ICU), 146 (12.9%) in a regular ward (RW) and 762 patients (67.2%) were at home. Hospitalized patients (RW and ICU) compared with patients from home showed a dramatically shorter 3-month survival (78.7% versus 94.4%), 1-year survival (66.3% versus 87.3%), and 3-year survival (61.7% versus 81.7%; all P 14 days, 60.5% versus 51.0%, P = 0.006). In conclusion, hospitalization status before transplantation is a valuable predictor of patient survival following LT

Feasibility and Efficacy of Adjuvant Chemotherapy With Gemcitabine After Liver Transplantation for Perihilar Cholangiocarcinoma: A Multi-Center, Randomized, Controlled Trial (pro-duct001)

Background Liver transplantation (LT) is considered a therapeutic option for unresectable perihilar cholangiocarcinoma (PHC) within defined criteria. It remains uncertain whether patients can safely receive adjuvant chemotherapy after LT. Methods We performed a prospective, multi-center, randomized, non-blinded two-arm trial (pro-duct001). Patients after LT for unresectable PHC within defined criteria were randomized to adjuvant gemcitabine (LT-Gem group) and LT alone (LT alone group). The primary objective was to investigate if adjuvant chemotherapy is feasible in ≥ 85% of patients after LT. The primary endpoint was the percentage of patients completing the 24 weeks course of adjuvant chemotherapy. Secondary endpoints included overall survival (OS) and disease-free (DFS), and complication rates. Results Twelve patients underwent LT for PHC, of which six (50%) were eligible for randomization (LT-Gem: three patients, LT alone: three patients). Two out of three patients discontinued adjuvant chemotherapy after LT due to intolerance. The study was prematurely terminated due to slow enrollment. One patient with PHC had underlying primary sclerosing cholangitis (PSC). Tumor-free margins could be achieved in all patients. In both the LT-Gem and the LT alone group, the cumulative 1-, 3-, and 5-year OS and DFS rates were 100%, 100%, 67%, and 100%, 67% and 67%, respectively. Conclusions This prospective, multi-center study was prematurely terminated due to slow enrollment and a statement on the defined endpoints cannot be made. Nevertheless, long-term survival data are consistent with available retrospective data and confirm defined criteria for LT. Since more evidence of LT per se in unresectable PHC is urgently needed, a prospective, non-randomized follow-up study (pro-duct002) has since been launched

Graph isomorphism is in the low hierarchy

AbstractIt is shown that the graph isomorphism problem is located in level L2p of the low hierarchy in NP. This implies that this problem is not NP-complete (even under weaker forms of polynomial reducibilities, like γ-reducibility) unless the polynomial-time hierarchy collapses to some finite level