Collective effects in tilted Weyl cones: optical conductivity, polarization, and Coulomb interactions reshaping the cone

Recently, the existence of Dirac/Weyl cones in three dimensional systems has been demonstrated experimentally. While in high energy physics the isotropy of the Dirac/Weyl cones is guaranteed by relativistic invariance, in condensed matter systems corrections to this can occur, one possible type being a tilt. In this paper we study the effect of of tilted Weyl cones in collective effects. We study both the opticql conductivity as well as the polarization function. We also investigate the perturbative effect of long-range Coulomb interactions using a renormalization group calculation. We find that the tilt is perturbatively renormalized towards zero and at low energies the system flows to an effectively untilted theory.Comment: 8 pages, 3 figure

Methods for integrating machine learning and constrained optimization

In the framework of industrial problems, the application of Constrained Optimization is known to have overall very good modeling capability and performance and stands as one of the most powerful, explored, and exploited tool to address prescriptive tasks. The number of applications is huge, ranging from logistics to transportation, packing, production, telecommunication, scheduling, and much more. The main reason behind this success is to be found in the remarkable effort put in the last decades by the OR community to develop realistic models and devise exact or approximate methods to solve the largest variety of constrained or combinatorial optimization problems, together with the spread of computational power and easily accessible OR software and resources. On the other hand, the technological advancements lead to a data wealth never seen before and increasingly push towards methods able to extract useful knowledge from them; among the data-driven methods, Machine Learning techniques appear to be one of the most promising, thanks to its successes in domains like Image Recognition, Natural Language Processes and playing games, but also the amount of research involved. The purpose of the present research is to study how Machine Learning and Constrained Optimization can be used together to achieve systems able to leverage the strengths of both methods: this would open the way to exploiting decades of research on resolution techniques for COPs and constructing models able to adapt and learn from available data. In the first part of this work, we survey the existing techniques and classify them according to the type, method, or scope of the integration; subsequently, we introduce a novel and general algorithm devised to inject knowledge into learning models through constraints, Moving Target. In the last part of the thesis, two applications stemming from real-world projects and done in collaboration with Optit will be presented

Teaching the Old Dog New Tricks: Supervised Learning with Constraints

Adding constraint support in Machine Learning has the potential to address outstanding issues in data-driven AI systems, such as safety and fairness. Existing approaches typically apply constrained optimization techniques to ML training, enforce constraint satisfaction by adjusting the model design, or use constraints to correct the output. Here, we investigate a different, complementary, strategy based on "teaching" constraint satisfaction to a supervised ML method via the direct use of a state-of-the-art constraint solver: this enables taking advantage of decades of research on constrained optimization with limited effort. In practice, we use a decomposition scheme alternating master steps (in charge of enforcing the constraints) and learner steps (where any supervised ML model and training algorithm can be employed). The process leads to approximate constraint satisfaction in general, and convergence properties are difficult to establish; despite this fact, we found empirically that even a na\"ive setup of our approach performs well on ML tasks with fairness constraints, and on classical datasets with synthetic constraints

Collective effects in tilted Weyl cones

Recently, the existence of Dirac/Weyl cones in three dimensional systems has been demonstrated experimentally. While in high energy physics the isotropy of the Dirac/Weyl cones is guaranteed by relativistic invariance, in condensed matter systems corrections to this can occur, one possible type being a tilt. In this paper we study the effect of of tilted Weyl cones in collective effects. We study both the opticql conductivity as well as the polarization function. We also investigate the perturbative effect of long-range Coulomb interactions using a renormalization group calculation. We find that the tilt is perturbatively renormalized towards zero and at low energies the system flows to an effectively untilted theory

District heating network maintenance planning optimization

To ensure the correct functioning of district heating networks and minimize critical failures, utilities allocate every year a significant part of their budget to maintenance operations. In the present work we describe a risk-based approach implemented to tackle the problem of designing optimal multi-year maintenance campaigns, applied to the Italian city of Brescia, showing how data-driven techniques can help decision makers assess the long terms impacts of budget allocations