Showing papers by "Paris Dauphine University published in 2015"

Many-Body Localization in Periodically Driven Systems

Abstract: We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases

Sliced and Radon Wasserstein Barycenters of Measures

Abstract: This article details two approaches to compute barycenters of measures using 1-D Wasserstein distances along radial projections of the input measures. The first method makes use of the Radon transform of the measures, and the second is the solution of a convex optimization problem over the space of measures. We show several properties of these barycenters and explain their relationship. We show numerical approximation schemes based on a discrete Radon transform and on the resolution of a non-convex optimization problem. We explore the respective merits and drawbacks of each approach on applications to two image processing problems: color transfer and texture mixing.

Virtual currency, tangible return: Portfolio diversification with bitcoin

Abstract: Bitcoin (BTC) is a major virtual currency. Using weekly data over the 2010-2013 period, we analyze a BTC investment from the standpoint of a US investor with a diversified portfolio including both traditional assets (worldwide stocks, bonds, hard currencies) and alternative investments (commodities, hedge funds, real estate). Over the period under consideration, BTC investment had highly distinctive features, including exceptionally high average return and volatility. Its correlation with other assets was remarkably low. Spanning tests confirm that BTC investment offers significant diversification benefits. We show that the inclusion of even a small proportion of BTCs may dramatically improve the risk-return trade-off of well-diversified portfolios. Results should however be taken with caution as the data may reflect early-stage behavior that may not last in the medium or long run.

Convolutional wasserstein distances: efficient optimal transportation on geometric domains

Abstract: This paper introduces a new class of algorithms for optimization problems involving optimal transportation over geometric domains. Our main contribution is to show that optimal transportation can be made tractable over large domains used in graphics, such as images and triangle meshes, improving performance by orders of magnitude compared to previous work. To this end, we approximate optimal transportation distances using entropic regularization. The resulting objective contains a geodesic distance-based kernel that can be approximated with the heat kernel. This approach leads to simple iterative numerical schemes with linear convergence, in which each iteration only requires Gaussian convolution or the solution of a sparse, pre-factored linear system. We demonstrate the versatility and efficiency of our method on tasks including reflectance interpolation, color transfer, and geometry processing.

Exponentially Slow Heating in Periodically Driven Many-Body Systems.

Abstract: We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including the decay of highly energetic excitations in cold atomic and solid-state systems.

Virtual Currency, Tangible Return: Portfolio Diversification with Bitcoin

Abstract: Bitcoin is a major virtual currency. Using weekly data over the 2010-2013 period, we analyze a Bitcoin investment from the standpoint of a U.S. investor with a diversified portfolio including both traditional assets (worldwide stocks, bonds, hard currencies) and alternative investments (commodities, hedge funds, real estate). Bitcoin investment has highly distinctive features, including exceptionally high average return and volatility. Its correlation with other assets is remarkably low. Spanning tests confirm that Bitcoin investment offers significant diversification benefits. We show that the inclusion of even a small proportion of Bitcoins, say 3%, may dramatically improve the risk-return trade-off of well-diversified portfolios.

Hypocoercivity for linear kinetic equations conserving mass

Abstract: We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models like the linear Boltzmann equation or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed.

Exact Support Recovery for Sparse Spikes Deconvolution

Abstract: This paper studies sparse spikes deconvolution over the space of measures We focus on the recovery properties of the support of the measure (ie, the location of the Dirac masses) using total variation of measures (TV) regularization This regularization is the natural extension of the $$\ell ^1$$l1 norm of vectors to the setting of measures We show that support identification is governed by a specific solution of the dual problem (a so-called dual certificate) having minimum $$L^2$$L2 norm Our main result shows that if this certificate is non-degenerate (see the definition below), when the signal-to-noise ratio is large enough TV regularization recovers the exact same number of Diracs We show that both the locations and the amplitudes of these Diracs converge toward those of the input measure when the noise drops to zero Moreover, the non-degeneracy of this certificate can be checked by computing a so-called vanishing derivative pre-certificate This proxy can be computed in closed form by solving a linear system Lastly, we draw connections between the support of the recovered measure on a continuous domain and on a discretized grid We show that when the signal-to-noise level is large enough, and provided the aforementioned dual certificate is non-degenerate, the solution of the discretized problem is supported on pairs of Diracs which are neighbors of the Diracs of the input measure This gives a precise description of the convergence of the solution of the discretized problem toward the solution of the continuous grid-free problem, as the grid size tends to zero

Arbitrage and Duality in Nondominated Discrete-Time Models

Abstract: We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum over the martingale measures. Moreover, we obtain a nondominated version of the Optional Decomposition Theorem.

Where the Risks Lie: A Survey on Systemic Risk

Abstract: We review the extensive literature on systemic risk and connect it to the current regulatory debate. While we take stock of the achievements of this rapidly growing field, we identify a gap between two main approaches. The first one studies different sources of systemic risk in isolation, uses confidential data, and inspires targeted but complex regulatory tools. The second approach uses market data to produce global measures which are not directly connected to any particular theory, but could support a more efficient regulation. Bridging this gap will require encompassing theoretical models and improved data disclosure.

Second order mean field games with degenerate diffusion and local coupling

Abstract: We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth, solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as minimizers of two optimal control problems. We also show that such solutions are stable with respect to the data, so that in particular the degenerate case can be approximated by a uniformly parabolic (viscous) perturbation.

Finding a collective set of items: from proportional multirepresentation to group recommendation

Abstract: We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of K items that maximize the total derived utility of all the agents (i.e., in our example we are to pick K movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Abstract: Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency $ u$. We prove that up to a quasi-exponential time $\tau_* \sim e^{c \frac{ u}{\log^3 u}}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $\hat D$ that governs the time evolution up to $\tau_*$, and hence this effective Hamiltonian is a conserved quantity up to $\tau_*$. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction $U$ is much larger than the hopping $J$. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time $\tau_*$ that is (almost) exponential in $U/J$.

Financial Flows and the International Monetary System

Abstract: We review the findings of the literature on the benefits of international financial flows and find that they are quantitatively elusive. We then present evidence on the existence of a global cycle in gross cross-border flows, asset prices and leverage and discuss its impact on monetary policy autonomy across different exchange rate regimes. We focus in particular on the effect of US monetary policy shocks on the UK's financial conditions.

Where the Risks Lie: A Survey on Systemic Risk

Abstract: We review the extensive literature on systemic risk and connect it to the current regulatory debate. While we take stock of the achievements of this rapidly growing field, we identify a gap between two main approaches. The first one studies different sources of systemic risk in isolation, uses confidential data, and inspires targeted but complex regulatory tools. The second approach uses market data to produce global measures which are not directly connected to any particular theory, but could support a more efficient regulation. Bridging this gap will require encompassing theoretical models and improved data disclosure.

Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations

Abstract: Many problems from mass transport can be reformulated as variational problems under a prescribed divergence constraint (static problems) or subject to a time-dependent continuity equation, which again can be formulated as a divergence constraint but in time and space. The variational class of mean field games, introduced by Lasry and Lions, may also be interpreted as a generalization of the time-dependent optimal transport problem. Following Benamou and Brenier, we show that augmented Lagrangian methods are well suited to treat such convex but non-smooth problems. They include in particular Monge historic optimal transport problem. A finite-element discretization and implementation of the method are used to provide numerical simulations and a convergence study.

Weak Solutions for First Order Mean Field Games with Local Coupling

Abstract: Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise e−Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) a time-space degenerate elliptic differential equation.

Gender diversity and board performance: women's experiences and perspectives

Abstract: Despite considerable progress that organizations have made during the past 20 years to increase the representation of women at board level, they still hold few board seats. Drawing on a qualitative study involving 30 companies with women directors in the United Kingdom, the United States, and Ghana, we investigate how the relationship between gender in the boardroom and corporate governance operates. The findings indicate that the presence of a minority of women on the board has an insignificant effect on board performance. Yet the chairperson's role is vital in leading the change for recruiting and evaluating candidates and their commitment to the board with diversity and governance in mind. Our study also sheds light on the multifaceted reasons why women directors appear to be resisting the discourse of gender quotas.

Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics

Abstract: We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function.

Quelle gouvernance pour les réseaux territorialisés d’organisations ?

Abstract: Pour de nombreux specialistes des reseaux territorialises, la question de leur gouvernance se pose de facon critique. Cependant, peu de travaux se sont focalises sur le sujet. Dans un contexte de multiplication de ce type de reseaux et devant les resultats mitiges des diverses experiences menees jusqu’a ce jour, cet article propose une synthese des connaissances et des pistes de formalisation d’une structure de gouvernance territoriale.

Crowding at the frontier: boundary spanners, gatekeepers and knowledge brokers

Abstract: Purpose – This paper aims to contribute to defining the concepts of boundary spanner, gatekeeper and knowledge broker. Design/methodology/approach – A review of the literature covering more than 100 sources. Findings – A review of past research leads to proposing a set of new definitions and also to the detection of six research avenues. Originality/value – The ability of organizations to recognize, source and integrate key information or knowledge is important for their strategy, innovation and performance over time. Three types of individuals have information gathering and knowledge dissemination roles at the frontier of organizations and groups: boundary spanners, gatekeepers and knowledge brokers. Although research on these individuals is well-developed, we found that in practice, the definitions of the concepts overlap and still need a clarification. So far, no systematic comparison of these roles has been undertaken.

Multiplicative stochastic heat equations on the whole space

Abstract: We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on $\mathbf{R}^3$, and on the other hand the KPZ equation on $\mathbf{R}$ via the Cole-Hopf transform. To perform these constructions, we adapt the theory of regularity structures to the setting of weighted Besov spaces. One particular feature of our construction is that it allows one to start both equations from a Dirac mass at the initial time.

Robust utility maximization in nondominated models with 2bsde: the uncertain volatility model

Abstract: The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is nondominated. We propose studying this problem in the framework of second-order backward stochastic differential equations (2BSDEs for short) with quadratic growth generators. We show for exponential, power, and logarithmic utilities that the value function of the problem can be written as the initial value of a particular 2BSDE and prove existence of an optimal strategy. Finally, several examples which shed more light on the problem and its links with the classical utility maximization one are provided. In particular, we show that in some cases, the upper bound of the volatility interval plays a central role, exactly as in the option pricing problem with uncertain volatility models.

The Sovereign Wealth Fund Discount: Evidence from Public Equity Investments

Abstract: We document that announcement-period abnormal returns of sovereign wealth fund (SWF) equity investments in publicly traded firms are positive but lower than those of comparable private investments. Further, SWF investment targets suffer from declining return on assets and sales growth over the following three years. Our results are robust to controls for target and deal characteristics and are not driven by SWF target selection criteria. Larger discounts are associated with SWFs taking seats on boards of directors and with SWFs under strict government control acquiring greater stakes, supporting the hypothesis that political influence negatively affects firm value and performance

A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

Abstract: This paper is devoted the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes. © 2013 Springer-Verlag Berlin Heidelberg.

Fast Optimal Transport Averaging of Neuroimaging Data

Abstract: Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before performing a linear group averaging. In this work we build on ideas originally introduced by Kantorovich [18] to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of the entropic smoothing approach used by [7]. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.