## Section: New Results

### Applications to Other Domains

Participants : Christelle Caillouet, David Coudert, Nicolas Nisse.

#### Unveiling Contacts within Macro-molecular assemblies by solving Minimum Weight Connectivity Inference Problems

Consider a set of oligomers listing the subunits involved in sub-complexes of a macro-molecular assembly, obtained e.g. using native mass spectrometry or affinity purification. Given these oligomers, connectivity inference (CI) consists in finding the most plausible contacts between these subunits, and minimum connectivity inference (MCI) is the variant consisting in finding a set of contacts of smallest cardinality. MCI problems avoid speculating on the total number of contacts, but yield a subset of all contacts and do not allow exploiting a priori information on the likelihood of individual contacts. In this context, we present in [15] two novel algorithms, MILP-W and MILP-WB. The former solves the minimum weight connectivity inference (MWCI), an optimization problem whose criterion mixes the number of contacts and their likelihood. The latter uses the former in a bootstrap fashion, to improve the sensitivity and the specificity of solution sets. Experiments on three systems (yeast exosome, yeast proteasome lid, human eiF3), for which reference contacts are known (crystal structure, cryo electron microscopy, cross-linking), show that our algorithms predict contacts with high specificity and sensitivity, yielding a very significant improvement over previous work, typically a twofold increase in sensitivity. The software accompanying this paper is made available, and should prove of ubiquitous interest whenever connectivity inference from oligomers is faced.

#### Recovery of Disrupted Airline Operations using $k$-Maximum Matching in Graphs

When an aircraft is approaching an airport, it gets a short time interval (called *slot*) that it can use to land. If the landing of the aircraft is delayed (because of bad weather, or if it arrives late, or if other aircrafts have to land first), it loses its slot and Air traffic controllers have to assign it a new slot. However, slots for landing are a scarce resource of the airports and, to avoid that an aircraft waits too much time, Air traffic controllers have to regularly modify the assignment of the slots of the aircrafts. Unfortunately, for legal and economical reasons, Air traffic controllers can modify the slot-assignment only using two kind of operations: either assign to aircraft $A$ a slot that was free, or give to $A$ the slot of another aircraft $B$ and assign to $B$ a free slot. The problem is then the following. Let $k\ge 1$ be an odd integer and let $G$ be a graph and $M$ be a matching (set of pairwise disjoint edges) of $G$. What is the maximum size of a matching that can be obtained from $M$ by using only augmenting paths of length at most $k$? Moreover, how to compute such a maximum matching? This problem has already been studied in the context of wireless networks, mainly because it provides a simple approximation for the classical matching problem. We prove in [65] , [49] that this problem can be solved in polynomial-time when $k\le 3$. Then, we show that, for any odd integer $k\ge 5$, the problem is NP-complete in planar bipartite graphs with maximum degree at most 3.

#### Inference of Curvilinear Structure based on Learning a Ranking Function and Graph Theory

To detect curvilinear structures in natural images, we propose in [63] a novel ranking learning system and an abstract curvilinear shape inference algorithm based on graph theory. We analyze the curvilinear structures as a set of small line segments. In this work, the rankings of the line segments are exploited to systematize the topological feature of the curvilinear structures. Structured Support Vector Machine is employed to learn the ranking function that predicts the correspondence of the given line segments and the latent curvilinear structures. We first extract curvilinear features using morphological profiles and steerable filtering responses. Also, we propose an orientation-aware feature descriptor and a feature grouping operator to improve the structural integrity during the learning process. To infer the curvilinear structure, we build a graph based on the output rankings of the line segments. We progressively reconstruct the curvilinear structure by looking for paths between remote vertices in the graph. Experimental results show that the proposed algorithm faithfully detects the curvilinear structures within various datasets.

#### Web Transparency for Complex Targeting: Algorithms, Limits, and Tradeoffs

Big Data promises important societal progress but exacerbates the need for due process and accountability. Companies and institutions can now discriminate between users at an individual level using collected data or past behavior. Worse, today they can do so in near perfect opacity. The nascent field of web transparency aims to develop the tools and methods necessary to reveal how information is used, however today it lacks robust tools that let users and investigators identify targeting using multiple inputs. In [67] , [38] , we formalize for the first time the problem of detecting and identifying targeting on combinations of inputs and provide the first algorithm that is asymptotically exact. This algorithm is designed to serve as a theoretical foundational block to build future scalable and robust web transparency tools. It offers three key properties. First, our algorithm is service agnostic and applies to a variety of settings under a broad set of assumptions. Second, our algorithm's analysis delineates a theoretical detection limit that characterizes which forms of targeting can be distinguished from noise and which cannot. Third, our algorithm establishes fundamental tradeoffs that lead the way to new metrics for the science of web transparency. Understanding the tradeoff between effective targeting and targeting concealment lets us determine under which conditions predatory targeting can be made unprofitable by transparency tools.