In these three lectures on quantum information and complexity, we will (1) review the basic concepts of quantum information processing units (QPUs), (2) prove a version of the claim that almost all quantum circuits are very complex in the sense that they are exponentially expensive to realize in the quantum circuit model of computation and (3) that the quantum complexity of a random quantum circuit grows linearly with the size of the circuit up to exponentially large circuits.

The underlying proof technique uses a versatile proof strategy from high-dimensional probability theory that can (and has been) readily extended to other problems within quantum computing theory and beyond.[-]

In these three lectures on quantum information and complexity, we will (1) review the basic concepts of quantum information processing units (QPUs), (2) prove a version of the claim that almost all quantum circuits are very complex in the sense that they are exponentially expensive to realize in the quantum circuit model of computation and (3) that the quantum complexity of a random quantum circuit grows linearly with the size of the circuit up to exponentially large circuits.

The underlying proof technique uses a versatile proof strategy from high-dimensional probability theory that can (and has been) readily extended to other problems within quantum computing theory and beyond.[-]

In these three lectures on quantum information and complexity, we will (1) review the basic concepts of quantum information processing units (QPUs), (2) prove a version of the claim that almost all quantum circuits are very complex in the sense that they are exponentially expensive to realize in the quantum circuit model of computation and (3) that the quantum complexity of a random quantum circuit grows linearly with the size of the circuit up to exponentially large circuits.

The underlying proof technique uses a versatile proof strategy from high-dimensional probability theory that can (and has been) readily extended to other problems within quantum computing theory and beyond.[-]

The post-surgical development of metastases (secondary tumors spread from a primary one) represents the major cause of death from a cancer disease. Mathematical models may have the potential to further assist in estimating metastatic risk, particularly when paired with in vivo tumor data that faithfully represent all stages of disease progression.
In this talk I will first describe a modeling approach that uses data from clinically relevant mouse models of spontaneous metastasis developing after surgical removal of orthotopically implanted primary tumors. Both presurgical (primary tumor) and postsurgical (metastatic) growth was quantified using bioluminescence. The model was able to fit and predict pre-/post-surgical data at the level of the individual as well as the population. Importantly, our approach also enabled retrospective analysis of clinical data describing the probability of metastatic relapse as a function of primary tumor size, where inter-individual variability was quantified by a key parameter of intrinsic metastatic potential. Critically, our analysis identified a highly nonlinear relationship between primary tumor size and postsurgical survival, suggesting possible threshold limits for the utility of tumor size as a predictor of metastatic recurrence.
In the second part of my talk, I will focus on some very intriguing phenomenon concerning systemic interactions between tumors within the organisms, termed “concomitant resistance”, by which, in the presence of two tumors, one inhibits the growth of the other. This has important clinical consequences as it can lead to post-surgery metastatic acceleration. Based on experimental data involving the simultaneous growth of two tumor implants, we will test biological theories underlying this process and establish a biologically relevant and minimally parameterized mathematical model.
These findings represent a novel use of clinically relevant models to assess the impact of surgery on metastatic potential and may guide optimal timing of treatments in neoadjuvant (presurgical) and adjuvant (postsurgical) settings to maximize patient benefit.[-]

In this talk, I will summarize some of our results on the properties of hippocampal place cells in rats that solve various spatial navigation tasks. Several of these properties are directly relevant to their role in navigation, including the phenomenon of local remapping, overdispersion (variability in firing), and goal-related firing, and thus emphasize the participation of place cells in the coding of spatial information and the computation of optimal paths.[-]

Start the video and click on the track button in the timeline to move to talk 1, 2 and to the discussion.

- Talk 1: Paul Apicella - Striatal dopamine and acetylcholine mechanisms involved in reward-related learning

The midbrain dopamine system has been identified as a major component of motivation and reward processing. One of its main targets is the striatum which plays an important role in motor control and learning functions. Other subcortical neurons work in parallel with dopamine neurons. In particular, striatal cholinergic interneurons participate in signaling the reward-related significance of stimuli and they may act in concert with dopamine to encode prediction error signals and control the learning of stimulus–response associations. Recent studies have revealed functional cooperativity between these two neuromodulatory systems of a complexity far greater than previously appreciated. In this talk I will review the difference and similarities between dopamine and acetylcholine reward-signaling systems, the possible nature of reward representation in each system, and discuss the involvement of striatal dopamine-acetylcholine interactions during leaning and behavior.

- Talk 2: Yonatan Loewenstein - Modeling operant learning: from synaptic plasticity to behavior

- Discussion with Paul Apicella and Yonatan Loewenstein[-]

Industrial strategic decisions have evolved tremendously in the last decades towards a higher degree of quantitative analysis. Such decisions require taking into account a large number of uncertain variables and volatile scenarios, much like financial market investments. Furthermore, they can be evaluated by comparing to portfolios of investments in financial assets such as in stocks, derivatives and commodity futures. This revolution led to the development of a new field of managerial science known as Real Options.
The use of Real Option techniques incorporates also the value of flexibility and gives a broader view of many business decisions that brings in techniques from quantitative finance and risk management. Such techniques are now part of the decision making process of many corporations and require a substantial amount of mathematical background. Yet, there has been substantial debate concerning the use of risk neutral pricing and hedging arguments to the context of project evaluation. We discuss some alternatives to risk neutral pricing that could be suitable to evaluation of projects in a realistic context with special attention to projects dependent on commodities and non-hedgeable uncertainties. More precisely, we make use of a variant of the hedged Monte-Carlo method of Potters, Bouchaud and Sestovic to tackle strategic decisions. Furthermore, we extend this to different investor risk profiles. This is joint work with Edgardo Brigatti, Felipe Macias, and Max O. de Souza.
If time allows we shall also discuss the situation when the historical data for the project evaluation is very limited and we can make use of certain symmetries of the problem to perform (with good estimates) a nonintrusive stratified resampling of the data. This is joint work with E. Gobet and G. Liu.[-]

Déléguer à une machine l'affectation des bacheliers dans le supérieur pose un certain nombre de questions : quels règles souhaite-t-on pour l'accès au supérieur ? Quels sont alors les objectifs assignés à la machine ? Quel algorithme permet de les atteindre ? Comment permettre à tous les citoyens de vérifier une exécution de l'algorithme ? On verra rapidement quels faux et vrais problèmes posait APB et pose Parcoursup. Je présenterai l'algorithme de Gale-Shapley et je montrerai comment on peut vérifier a posteriori que cet algorithme a été exécuté correctement, de façon plus ou moins complète selon le degré d'anonymat des candidatures et des classements.

In France, matching students who have passed the baccalaureat to higher education is a computer-based process. A new process is being used this year. Some questions arise: what are the rules that determine access to higher education? What goal is the computer-based process supposed to be aimed at? By what means? How are citizens allowed to check that the process runs smoothly and gives equitable results? This talk reviews some of the issues raised by both the former and the new processes, introduces the Gale-Shapley algorithm and explains how a run of the process can be independently verified.[-]

The emergence of drug-resistance is a major challenge in chemotherapy. In this talk we will present our recent mathematical models for describing the dynamics of drug-resistance in solid tumors. Our models follow the dynamics of the tumor, assuming that the cancer cell population depends on a phenotype variable that corresponds to the resistance level to a cytotoxic drug. We incorporate the dynamics of nutrients and two different types of drugs: a cytotoxic drug, which directly impacts the death rate of the cancer cells, and a cytostatic drug that reduces the proliferation rate. Through analysis and simulations, we study the impact of spatial and phenotypic heterogeneity on the tumor growth under chemotherapy. We demonstrate that heterogeneous cancer cells may emerge due to the selection dynamics of the environment. Our models predict that under certain conditions, multiple resistant traits emerge at different locations within the tumor. We show that a higher dosage of the cytotoxic drug may delay a relapse, yet, when this happens, a more resistant trait emerges. Moreover, we estimate the expansion rate of the tumor boundary as well as the time of relapse, in terms of the resistance trait, the level of the nutrient, and the drug concentration. Finally, we propose an efficient drug schedule aiming at minimizing the growth rate of the most resistant trait. By combining the cytotoxic and cytostatic drugs, we demonstrate that the resistant cells can be eliminated.[-]