Approximation Hardness of Graphic TSP on Cubic Graphs

We prove explicit approximation hardness results for the Graphic TSP on cubic and subcubic graphs as well as the new inapproximability bounds for the corresponding instances of the (1,2)-TSP. The proof technique uses new modular constructions of simulating gadgets for the restricted cubic and subcubic instances. The modular constructions used in the paper could be also of independent interest

New Inapproximability Bounds for TSP

In this paper, we study the approximability of the metric Traveling Salesman Problem (TSP) and prove new explicit inapproximability bounds for that problem. The best up to now known hardness of approximation bounds were 185/184 for the symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to Papadimitriou and Vempala). We construct here two new bounded occurrence CSP reductions which improve these bounds to 123/122 and 75/74, respectively. The latter bound is the first improvement in more than a decade for the case of the asymmetric TSP. One of our main tools, which may be of independent interest, is a new construction of a bounded degree wheel amplifier used in the proof of our results

Approximating Subdense Instances of Covering Problems

We study approximability of subdense instances of various covering problems on graphs, defined as instances in which the minimum or average degree is Omega(n/psi(n)) for some function psi(n)=omega(1) of the instance size. We design new approximation algorithms as well as new polynomial time approximation schemes (PTASs) for those problems and establish first approximation hardness results for them. Interestingly, in some cases we were able to prove optimality of the underlying approximation ratios, under usual complexity-theoretic assumptions. Our results for the Vertex Cover problem depend on an improved recursive sampling method which could be of independent interest

On Approximability of Bounded Degree Instances of Selected Optimization Problems

In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation algorithms for the restricted version of the problem with improved performance guarantees. In this thesis, we investigate the approximation complexity of selected NP-hard optimization problems restricted to instances with bounded degree, occurrence or weight parameter. Specifically, we consider the family of dense instances, where typically the average degree is bounded from below by some function of the size of the instance. Complementarily, we examine the family of sparse instances, in which the average degree is bounded from above by some fixed constant. We focus on developing new methods for proving explicit approximation hardness results for general as well as for restricted instances. The fist part of the thesis contributes to the systematic investigation of the VERTEX COVER problem in k-hypergraphs and k-partite k-hypergraphs with density and regularity constraints. We design efficient approximation algorithms for the problems with improved performance guarantees as compared to the general case. On the other hand, we prove the optimality of our approximation upper bounds under the Unique Games Conjecture or a variant. In the second part of the thesis, we study mainly the approximation hardness of restricted instances of selected global optimization problems. We establish improved or in some cases the first inapproximability thresholds for the problems considered in this thesis such as the METRIC DIMENSION problem restricted to graphs with maximum degree 3 and the (1,2)-STEINER TREE problem. We introduce a new reductions method for proving explicit approximation lower bounds for problems that are related to the TRAVELING SALESPERSON (TSP) problem. In particular, we prove the best up to now inapproximability thresholds for the general METRIC TSP problem, the ASYMMETRIC TSP problem, the SHORTEST SUPERSTRING problem, the MAXIMUM TSP problem and TSP problems with bounded metrics

Isolation of human MHC class II-restricted T cell receptors from the autologous T-cell repertoire with potent anti-leukaemic reactivity

Summary Adoptive transfer of T cells genetically modified with tumour-specific T-cell receptors (TCR) is a promising novel approach in the treatment of cancer. We have previously isolated an allorestricted MHC class I-restricted TCR with specificity for Formin-like protein 1 (FMNL1) with potent activity against chronic lymphocytic leukaemia cells. CD4 + T cells have been described to be highly important for tumour elimination although TCR derived from CD4 + T cells with anti-tumour reactivity have been only rarely described. In this study we aimed to isolate MHC class-II-restricted CD4 + T cells and TCR with specificity for leukaemia antigens. We used professional antigen-presenting cells pulsed with the leukaemiaassociated and tumour-associated antigen FMNL1 for stimulation of autologous T cells in vitro. We isolated two CD4 + HLA-DR-restricted T-cell clones and T-cell-derived TCR with so far unknown specificity but high reactivity against lymphoma cells and native malignant cells derived from HLA-matched patients with diverse leukaemias. Moreover, characterization of the TCR after TCR gene transfer revealed that specific characteristics of isolated TCR as reactivity in response to Toll-like receptors were transferable on effector cells. Our results have a major impact on the development of novel immunotherapies. They demonstrate that TCR with potent HLA-DR-restricted anti-leukaemic reactivity against so far undefined self-restricted antigens can be isolated from the healthy autorestricted CD4 + T-cell repertoire and these TCR are highly interesting candidate tools for novel immunotherapies

Assessing the impacts of 1.5 °C global warming – simulation protocol of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP2b)

In Paris, France, December 2015, the Conference of the Parties (COP) to the United Nations Framework Convention on Climate Change (UNFCCC) invited the Intergovernmental Panel on Climate Change (IPCC) to provide a "special report in 2018 on the impacts of global warming of 1.5°C above pre-industrial levels and related global greenhouse gas emission pathways". In Nairobi, Kenya, April 2016, the IPCC panel accepted the invitation. Here we describe the response devised within the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) to provide tailored, cross-sectorally consistent impact projections to broaden the scientific basis for the report. The simulation protocol is designed to allow for (1) separation of the impacts of historical warming starting from pre-industrial conditions from impacts of other drivers such as historical land-use changes (based on pre-industrial and historical impact model simulations); (2) quantification of the impacts of additional warming up to 1.5°C, including a potential overshoot and long-term impacts up to 2299, and comparison to higher levels of global mean temperature change (based on the low-emissions Representative Concentration Pathway RCP2.6 and a no-mitigation pathway RCP6.0) with socio-economic conditions fixed at 2005 levels; and (3) assessment of the climate effects based on the same climate scenarios while accounting for simultaneous changes in socio-economic conditions following the middle-of-the-road Shared Socioeconomic Pathway (SSP2, Fricko et al., 2016) and in particular differential bioenergy requirements associated with the transformation of the energy system to comply with RCP2.6 compared to RCP6.0. With the aim of providing the scientific basis for an aggregation of impacts across sectors and analysis of cross-sectoral interactions that may dampen or amplify sectoral impacts, the protocol is designed to facilitate consistent impact projections from a range of impact models across different sectors (global and regional hydrology, lakes, global crops, global vegetation, regional forests, global and regional marine ecosystems and fisheries, global and regional coastal infrastructure, energy supply and demand, temperature-related mortality, and global terrestrial biodiversity)