Partial recovery bounds for clustering with the relaxed KKmeans

We investigate the clustering performances of the relaxed $K$means in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the misclassification error decay exponentially fast with respect to this SNR. These partial recovery bounds for the relaxed $K$means improve upon results currently known in the sGMM setting. In the SBM setting, applying the relaxed $K$means SDP allows to handle general connection probabilities whereas other SDPs investigated in the literature are restricted to the assortative case (where within group probabilities are larger than between group probabilities). Again, this partial recovery bound complements the state-of-the-art results. All together, these results put forward the versatility of the relaxed $K$means.Comment: 39 page

Error structures and parameter estimation

This article proposes a link between statistics and the theory of Dirichlet forms used to compute errors. The error calculus based on Dirichlet forms is an extension of classical Gauss' approach to error propagation. The aim of this paper is to derive error structures from measurements. The links with Fisher's information lay the foundations of a strong connection with experiment. We show that this connection behaves well towards changes of variables and is related to the theory of asymptotic statistics

The four-in-a-tree problem in triangle-free graphs

The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time O(n4) whether three given vertices of a graph belong to an induced tree. Here, we study four-in-a-tree for triangle-free graphs. We give a structural answer to the following question : how does look like a triangle-free graph such that no induced tree covers four given vertices ? Our main result says that any such graph must have the "same structure", in a sense to be defined precisely, as a square or a cube. We provide an O(nm)-time algorithm that given a triangle-free graph G together with four vertices outputs either an induced tree that contains them or a partition of V(G) certifying that no such tree exists. We prove that the problem of deciding whether there exists a tree T covering the four vertices such that at most one vertex of T has degree at least 3 is NP-complete.Three, four, tree, algorithm, 3-in-a-tree, 4-in-a-tree, triangle-free graphs.

Heralded single phonon preparation, storage and readout in cavity optomechanics

We analyze theoretically how to use the radiation pressure coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state), and release on-demand the stored excitation as a single photon. Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband leads to dynamical backaction amplification and to the creation of correlated photon-phonon pairs. The detection of one Stokes photon thus projects the macroscopic oscillator into a single-phonon Fock state. The non-classical nature of this mechanical state can be demonstrated by applying a readout laser on the lower sideband (i.e. optical cooling) to map the phononic state to a photonic mode, and by performing an autocorrelation measurement on the anti-Stokes photons. We discuss the relevance of our proposal for the future of cavity optomechanics as an enabling quantum technology.Comment: Accepted for publication in Physical Review Letters. Added References 42,4

Factorial moments of point processes

We derive joint factorial moment identities for point processes with Papangelou intensities. Our proof simplifies previous approaches to related moment identities and includes the setting of Poisson point processes. Applications are given to random transformations of point processes and to their distribution invariance properties

Metrics and causality on Moyal planes

Metrics structures stemming from the Connes distance promote Moyal planes to the status of quantum metric spaces. We discuss this aspect in the light of recent developments, emphasizing the role of Moyal planes as representative examples of a recently introduced notion of quantum (noncommutative) locally compact space. We move then to the framework of Lorentzian noncommutative geometry and we examine the possibility of defining a notion of causality on Moyal plane, which is somewhat controversial in the area of mathematical physics. We show the actual existence of causal relations between the elements of a particular class of pure (coherent) states on Moyal plane with related causal structure similar to the one of the usual Minkowski space, up to the notion of locality.Comment: 33 pages. Improved version; a summary added at the end of the introduction, misprints corrected. Version to appear in Contemporary Mathematic

Predicting customer wallet without survey data.

A single company provides only a part of the total volume of products or services required by a customer. From the company perspective, this total business volume conducted by a customer, the customer's Size-of-Wallet, is generally unobservable. The percentage of this business done with the company, the customer's Share-of-Wallet, is unobservable as well. This paper focuses on the prediction of these values and on the derived concept of Potential-of-Wallet, which is the di®erence between the Size-of-Wallet and the actual business volume the customer does with the focal company. In the existing literature, the models predicting the customer wallet need survey data to estimate the model parameters. We propose an approach to predicting customer wallet without using survey data. In the empirical application, we show that a company can generate substantial gains by targeting customers with a large Potential-of-Wallet.Customer relationship management; Prediction; Retail banking; Share-of-wallet;

Development of a micromechanical model in interaction with parameters related to the microstructure of carbon/epoxy composites.

Gaseous Hydrogen storage under high pressure for autonomous energy application leads to non-metallic solutions for the material of vessels. The choice of wound carbon / epoxy composites was adopted for the design of storage tanks under high pressure. In this paper, the development of a micromechanical model in interaction with the microstructure parameters is presented. First a finite element analysis (FEA) allows us to perform numerical simulations on a representative volume cell based on observed microstructure to determine the local mechanical response. Then a parametric study is done. It reveals the effects of the voids on the mechanical properties. These effects identification and evaluation will be the basics knowledge bricks to build a guide design and process improvements for the vessel dome behaviours

Predicting customer wallet without survey data.

Each consumer requires a certain quantity of services or products, and a single company usually provides only a part of this. In the banking sector, the total quantity of business a customer does is called the Size-of-Wallet of this customer and it is generally unobservable. From a company perspective, the percentage of this business done with the company is called the Share-of-Wallet of this customer and is usually unobservable as well. This paper focuses on the prediction of these values and on the derived concept of Potential-of-Wallet, which is the difference between the Size-of-Wallet and the actual business the customer does with the focal company. In the existing literature, the models predicting the customer's wallet need survey data to estimate the model parameters. The main contribution of this paper is to propose an approach to predict the customer's wallet without using survey data. In the empirical application, we show that a company can generate substantial gains by targeting customers having a large Potential-of-Wallet.Customer relationship management; Prediction; Retail banking; Share-of-Wallet;