Combinatorics of the Permutahedra, Associahedra, and Friends

I present an overview of the research I have conducted for the past ten years in algebraic, bijective, enumerative, and geometric combinatorics. The two main objects I have studied are the permutahedron and the associahedron as well as the two partial orders they are related to: the weak order on permutations and the Tamari lattice. This document contains a general introduction (Chapters 1 and 2) on those objects which requires very little previous knowledge and should be accessible to non-specialist such as master students. Chapters 3 to 8 present the research I have conducted and its general context. You will find: * a presentation of the current knowledge on Tamari interval and a precise description of the family of Tamari interval-posets which I have introduced along with the rise-contact involution to prove the symmetry of the rises and the contacts in Tamari intervals; * my most recent results concerning q, t-enumeration of Catalan objects and Tamari intervals in relation with triangular partitions; * the descriptions of the integer poset lattice and integer poset Hopf algebra and their relations to well known structures in algebraic combinatorics; * the construction of the permutree lattice, the permutree Hopf algebra and permutreehedron; * the construction of the s-weak order and s-permutahedron along with the s-Tamari lattice and s-associahedron. Chapter 9 is dedicated to the experimental method in combinatorics research especially related to the SageMath software. Chapter 10 describes the outreach efforts I have participated in and some of my approach towards mathematical knowledge and inclusion.Comment: 163 pages, m\'emoire d'Habilitation \`a diriger des Recherche

Genetically modified organisms for the environment: stories of success and failure and what we have learned from them

The expectations raised in the mid-1980s on the potential of genetic engineering for in situ remediation of environmental pollution have not been entirely fulfilled. Yet, we have learned a good deal about the expression of catabolic pathways by bacteria in their natural habitats, and how environmental conditions dictate the expression of desired catalytic activities. The many different choices between nutrients and responses to stresses form a network of transcriptional switches which, given the redundance and robustness of the regulatory circuits involved, can be neither unraveled through standard genetic analysis nor artificially programmed in a simple manner. Available data suggest that population dynamics and physiological control of catabolic gene expression prevail over any artificial attempt to engineer an optimal performance of the wanted catalytic activities. In this review, several valuable spin-offs of past research into genetically modified organisms with environmental applications are discussed, along with the impact of Systems Biology and Synthetic Biology in the future of environmental biotechnology. [Int Microbiol 2005; 8(3):213-222

Space biology initiative program definition review. Trade study 2: Prototype utilization in the development of space biology hardware

The objective was to define the factors which space flight hardware developers and planners should consider when determining: (1) the number of hardware units required to support program; (2) design level of the units; and (3) most efficient means of utilization of the units. The analysis considered technology risk, maintainability, reliability, and safety design requirements for achieving the delivery of highest quality flight hardware. Relative cost impacts of the utilization of prototyping were identified. The development of Space Biology Initiative research hardware will involve intertwined hardware/software activities. Experience has shown that software development can be an expensive portion of a system design program. While software prototyping could imply the development of a significantly different end item, an operational system prototype must be considered to be a combination of software and hardware. Hundreds of factors were identified that could be considered in determining the quantity and types of prototypes that should be constructed. In developing the decision models, these factors were combined and reduced by approximately ten-to-one in order to develop a manageable structure based on the major determining factors. The Baseline SBI hardware list of Appendix D was examined and reviewed in detail; however, from the facts available it was impossible to identify the exact types and quantities of prototypes required for each of these items. Although the factors that must be considered could be enumerated for each of these pieces of equipment, the exact status and state of development of the equipment is variable and uncertain at this time

Data-driven solutions to enhance planning, operation and design tools in Industry 4.0 context

This thesis proposes three different data-driven solutions to be combined to state-of-the-art solvers and tools in order to primarily enhance their computational performances. The problem of efficiently designing the open sea floating platforms on which wind turbines can be mount on will be tackled, as well as the tuning of a data-driven engine's monitoring tool for maritime transportation. Finally, the activities of SAT and ASP solvers will be thoroughly studied and a deep learning architecture will be proposed to enhance the heuristics-based solving approach adopted by such software. The covered domains are different and the same is true for their respective targets. Nonetheless, the proposed Artificial Intelligence and Machine Learning algorithms are shared as well as the overall picture: promote Industrial AI and meet the constraints imposed by Industry 4.0 vision. The lesser presence of human-in-the-loop, a data-driven approach to discover causalities otherwise ignored, a special attention to the environmental impact of industries' emissions, a real and efficient exploitation of the Big Data available today are just a subset of the latter. Hence, from a broader perspective, the experiments carried out within this thesis are driven towards the aforementioned targets and the resulting outcomes are satisfactory enough to potentially convince the research community and industrialists that they are not just "visions" but they can be actually put into practice. However, it is still an introduction to the topic and the developed models are at what can be defined a "pilot" stage. Nonetheless, the results are promising and they pave the way towards further improvements and the consolidation of the dictates of Industry 4.0

Atomic scale modeling of ordering phenomena

Ordering phenomena in materials often have a crucial impact on materials properties.They are governed by the competition between entropy and energy.Accordingly simulating these aspects requires the construction of models that enable a computationally efficient exploration of the relevant configuration space.The alloy cluster expansion technique is particular well suited for this task as they can be trained to reach high accuracy while being computationally suitable for rapid sampling via Monte Carlo simulations. In paper I we present the icet software for the construction and sampling of alloy cluster expansions.In this thesis the alloy cluster expansion method is applied to study several different materials. The first group of materials studied are inorganic clathrates.In paper II and III we studied the ordering behavior and related properties as a function of composition and temperature for the clathrates Ba8AlxSi46-x, Ba8AlxGe46-x, Ba8GaxGe46-x, and Ba8GaxSi46-x.We achieved very good agreement with the available experimental data for the site occupancy factors (SOFs). In paper IV and V we constructed the phase diagram for the W-Ti and W-C system respectively.A cluster expansion for each system was constructed and the configurational free energy was calculated.By also including other contributions to the free energy, most notably the vibrational free energy, the phase diagrams for these systems could be constructed. In paper VI we studied the SSZ-13 zeolite and showed both that the L\uf6wenstein rule is not respected with hydrogen as counterion and provided a rationale for this behavior

Multilabel Classification Models for the Prediction of Cross-Coupling Reaction Conditions

Machine-learned ranking models have been developed for the prediction of substrate-specific cross-coupling reaction conditions. Data sets of published reactions were curated for Suzuki, Negishi, and C–N couplings, as well as Pauson–Khand reactions. String, descriptor, and graph encodings were tested as input representations, and models were trained to predict the set of conditions used in a reaction as a binary vector. Unique reagent dictionaries categorized by expert-crafted reaction roles were constructed for each data set, leading to context-aware predictions. We find that relational graph convolutional networks and gradient-boosting machines are very effective for this learning task, and we disclose a novel reaction-level graph attention operation in the top-performing model

Multilabel Classification Models for the Prediction of Cross-Coupling Reaction Conditions

Machine-learned ranking models have been developed for the prediction of substrate-specific cross-coupling reaction conditions. Data sets of published reactions were curated for Suzuki, Negishi, and C–N couplings, as well as Pauson–Khand reactions. String, descriptor, and graph encodings were tested as input representations, and models were trained to predict the set of conditions used in a reaction as a binary vector. Unique reagent dictionaries categorized by expert-crafted reaction roles were constructed for each data set, leading to context-aware predictions. We find that relational graph convolutional networks and gradient-boosting machines are very effective for this learning task, and we disclose a novel reaction-level graph attention operation in the top-performing model