Robust Flows over Time: Models and Complexity Results

We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a certain travel time to traverse an edge. In our setting, we account for uncertain travel times of flow. We investigate maximum flows over time under the assumption that at most $\Gamma$ travel times may be prolonged simultaneously due to delay. We develop and study a mathematical model for this problem. As the dynamic robust flow problem generalizes the static version, it is NP-hard to compute an optimal flow. However, our dynamic version is considerably more complex than the static version. We show that it is NP-hard to verify feasibility of a given candidate solution. Furthermore, we investigate temporally repeated flows and show that in contrast to the non-robust case (that is, without uncertainties) they no longer provide optimal solutions for the robust problem, but rather yield a worst case optimality gap of at least $T$. We finally show that the optimality gap is at most $O(\eta k \log T)$, where $\eta$ and $k$ are newly introduced instance characteristics and provide a matching lower bound instance with optimality gap $\Omega(\log T)$ and $\eta = k = 1$. The results obtained in this paper yield a first step towards understanding robust dynamic flow problems with uncertain travel times

Inhibition of MYC translation through targeting of the newly identified PHB-eIF4F complex as therapeutic strategy in CLL

Dysregulation of messenger RNA (mRNA) translation, including preferential translation of mRNA with complex 5′ untranslated regions such as the MYC oncogene, is recognized as an important mechanism in cancer. Here, we show that both human and murine chronic lymphocytic leukemia (CLL) cells display a high translation rate, which is inhibited by the synthetic flavagline FL3, a prohibitin (PHB)-binding drug. A multiomics analysis performed in samples from patients with CLL and cell lines treated with FL3 revealed the decreased translation of the MYC oncogene and of proteins involved in cell cycle and metabolism. Furthermore, inhibiting translation induced a proliferation arrest and a rewiring of MYC-driven metabolism. Interestingly, contrary to other models, the RAS-RAF-(PHBs)-MAPK pathway is neither impaired by FL3 nor implicated in translation regulation in CLL cells. Here, we rather show that PHBs are directly associated with the eukaryotic initiation factor (eIF)4F translation complex and are targeted by FL3. Knockdown of PHBs resembled FL3 treatment. Importantly, inhibition of translation controlled CLL development in vivo, either alone or combined with immunotherapy. Finally, high expression of translation initiation–related genes and PHBs genes correlated with poor survival and unfavorable clinical parameters in patients with CLL. Overall, we demonstrated that translation inhibition is a valuable strategy to control CLL development by blocking the translation of several oncogenic pathways including MYC. We also unraveled a new and direct role of PHBs in translation initiation, thus creating new therapeutic opportunities for patients with CLL

Caractérisation du microenvironnement tumoral dans la leucémie lymphoïde chronique par cytométrie de masse : implications pour l'immunothérapie

Chronic lymphocytic leukemia (CLL), the most frequent leukemia in adults, is characterized by the accumulation of mature B lymphocytes in peripheral blood and lymphoid tissues. The progression of CLL is highly dependent on complex interactions within the tumor microenvironment (TME) and despite recent advances in CLL treatment targeting the TME, CLL remains an incurable disease. Therefore, we wanted to deeply characterize the immune landscape in the TME in murine and human CLL to identify novel potential targets for an immunotherapeutic approach. For this purpose, we performed a comprehensive and extensive characterization by high-dimensional mass cytometry to establish an extensive cartography of immune cell subsets. We demonstrated that relevant changes in the immune cell composition, especially the expansion of specific lymphoid and myeloid immune cell subsets, are associated with strong immune suppression thereby contributing to an escape phenotype in CLL. These CLL-associated changes can be restored in preclinical models by a dual PD1/LAG3 immune checkpoint blockade. Moreover, we demonstrated a high T cell heterogeneity between patients that can be stratified according to their T cell profile, and the correlation of specific T cell subsets with time to initial treatment, highlighting their potential prognostic value. In conclusion, with this first CyTOF study in CLL, we expanded the current knowledge of the phenotypic complexity of the TME. We demonstrated that dual targeting of immune checkpoints efficiently controlled CLL development in preclinical models and therefore could have potential benefits in CLL to restore a functional anti-tumor immunity.La leucémie lymphoïde chronique (LLC), la leucémie la plus fréquente chez l'adulte, est caractérisée par l'accumulation de lymphocytes B matures dans le sang périphérique et les tissus lymphoïdes. La progression de la LLC est fortement dépendante des interactions complexes au sein du microenvironnement tumoral (TME) et malgré les récentes avancées dans le traitement de la LLC ciblant la TME, la LLC reste une maladie incurable. Par conséquent, nous voulions caractériser en profondeur le paysage immunitaire dans le TME dans la LLC murine et humaine afin d'identifier de nouvelles cibles potentielles pour une approche immunothérapeutique. À cette fin, nous avons effectué une caractérisation complète et approfondie par cytométrie de masse à haute dimension pour établir une cartographie approfondie des sous-populations de cellules immunitaires. Nous démontrons que les changements pertinents dans la composition des cellules immunitaires, en particulier l'expansion de sous-populations spécifiques de cellules immunitaires lymphoïdes et myéloïdes, sont associés à une forte suppression immunitaire contribuant ainsi à un phénotype d'échappement dans la LLC. Ces changements associés à la LLC peuvent être restaurés dans les modèles précliniques par un double blocage du point de contrôle immunitaire PD1/LAG3. De plus, nous démontrons une forte hétérogénéité des cellules T entre les patients qui peut être stratifiée en fonction de leur profil de cellules T, et la corrélation de sous-ensembles de cellules T spécifiques avec le temps jusqu'au traitement initial, mettant en évidence leur valeur pronostique potentielle. En conclusion, avec cette première étude CyTOF dans la LLC, nous avons élargi les connaissances actuelles sur la complexité phénotypique du TME. Nous avons démontré que le double ciblage des points de contrôle immunitaires contrôlait efficacement le développement de la LLC dans les modèles précliniques et pouvait donc avoir des avantages potentiels dans la LLC pour restaurer une immunité anti-tumorale fonctionnelle

Algorithms and complexity results for packing and covering problems and robust dynamic network flows under primal-dual aspects

Primal-dual methods have a longstanding history as a tool which proves approximation guarantees for solutions to combinatorial optimization problems. These methods also play a central role in this work. In this thesis, we investigate a general class of weighted covering problems, and static and dynamic network flow problems under uncertainty. We provide new theoretic insights and design approximation algorithms for both problems. For weighted covering problems, we focus on the characterization of a subclass of instances for which the primal-dual greedy algorithm is a viable solution strategy. For network flow problems, we evaluate classical solution concepts under uncertainty, that is, when edges fail in the static case and when edges are subject to delays in the dynamic setting. We call a combinatorial optimization problem a weighted covering problem if it can be written in the form \min_{x \in \ZZ_+^n} \left\{ c^T x \mid Ax \geq r \right\}, where A \in \RR_+^{m \times n}, r \in \RR^m and c \in \RR_+^n. That is, in weighted covering problems, we seek to find integer vectors which are feasible for an inequality system with non-negative coefficients and which minimize a linear objective function. Famous examples include various network design problems, vertex cover, knapsack cover, and optimization over polymatroids. Many covering problems are accompanied by a very simple algorithmic approach which obtains approximate solutions: the primal-dual greedy algorithm. Our main result is the characterization of a subclass of weighted covering problems for which the primal-dual greedy algorithm is proven to (1) always obtain a feasible solution which (2) has a bounded approximation guarantee. Our framework describes the approximation guarantee in terms of characteristics of the inequality system $(A,r)$ and independent of the cost function $c$. For many problems, including the list of examples above, the bounds from our framework match the best known results from the literature. It also covers new results, proving approximation guarantees for the precedence constrained knapsack cover problem and for a natural generalization of the flow cover on a line problem. Our characterization is smallest possible in the sense that the removal of any one of the required properties results in a situation in which the analyzed primal-dual greedy algorithm no longer necessarily computes feasible solutions. In the second part of this thesis, we discuss static and dynamic maximum flow problems under uncertainty. In the static maximum flow problem, the goal is to maximize the total throughput in a capacitated network. The dynamic variant considers an additional temporal component and the goal is to maximize the throughput within a given time horizon while flow takes time in order to traverse the network. In our results, we consider these problems subject to uncertain input data. That is, we seek to find solutions which are robust against edge failures and edge delays, respectively, in the static and dynamic case. In either case, solutions are evaluated under a robust worst-case perspective. For the static maximum flow problem subject to uncertainty, our main contribution is the introduction of a hybrid model and its analysis. The model contains the $\Gamma$-robust maximum flow problem and a stochastic variant as its extremes. For this hybrid model, we analyze the quality of solutions when a full characterization of the probability distribution of the stochastic model is unknown and only a small sample is available. In the dynamic variant, we first introduce a $\Gamma$-robust model and discuss generalizations of classical solution concepts. Our main contribution is the analysis of the solution quality of temporally repeated solutions under uncertainty. It is well-known that the class of temporally repeated solutions is optimum if all input data is certain. Under uncertainty, we show that this is no longer the case by providing lower and upper bounds on the optimality gap of temporally repeated solutions, when compared to general solutions