Simulation of quantum walks and fast mixing with classical processes

We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains (LMCs), that is, classical Markov chains with added memory. We show that LMCs can simulate the mixing behavior of any quantum walk, under a commonly satisfied invariance condition. This allows us to answer an open question on how the graph topology ultimately bounds a quantum walk's mixing performance, and that of any stochastic local evolution. The results highlight that speedups in mixing and transport phenomena are not necessarily diagnostic of quantum effects, although superdiffusive spreading is more prominent with quantum walks. The general simulating LMC construction may lead to large memory, yet we show that for the main graphs under study (i.e., lattices) this memory can be brought down to the same size employed in the quantum walks proposed in the literature

Many-to-Many Graph Matching: a Continuous Relaxation Approach

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a graph matching problem where one seeks a mapping between vertices of two graphs which optimally aligns their structure. In the classical formulation of graph matching, only one-to-one correspondences between vertices are considered. However, in many applications, graphs cannot be matched perfectly and it is more interesting to consider many-to-many correspondences where clusters of vertices in one graph are matched to clusters of vertices in the other graph. In this paper, we formulate the many-to-many graph matching problem as a discrete optimization problem and propose an approximate algorithm based on a continuous relaxation of the combinatorial problem. We compare our method with other existing methods on several benchmark computer vision datasets.Comment: 1

Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that propagate and create shocks. We propose a new approach based on the kinetic description of the conservation law. A kinetic equation is a first order partial differential equation in which the advection velocity is a free variable. In certain cases, it is possible to prove that the nonlinear conservation law is equivalent to a linear kinetic equation. Hence, data assimilation is carried out at the kinetic level, using a Luenberger observer also known as the nudging strategy in data assimilation. Assimilation then resumes to the handling of a BGK type equation. The advantage of this framework is that we deal with a single "linear" equation instead of a nonlinear system and it is easy to recover the macroscopic variables. The study is divided into several steps and essentially based on functional analysis techniques. First we prove the convergence of the model towards the data in case of complete observations in space and time. Second, we analyze the case of partial and noisy observations. To conclude, we validate our method with numerical results on Burgers equation and emphasize the advantages of this method with the more complex Saint-Venant system

Back-pressure traffic signal control with unknown routing rates

The control of a network of signalized intersections is considered. Previous works proposed a feedback control belonging to the family of the so-called back-pressure controls that ensures provably maximum stability given pre-specified routing probabilities. However, this optimal back-pressure controller (BP*) requires routing rates and a measure of the number of vehicles queuing at a node for each possible routing decision. It is an idealistic assumption for our application since vehicles (going straight, turning left/right) are all gathered in the same lane apart from the proximity of the intersection and cameras can only give estimations of the aggregated queue length. In this paper, we present a back-pressure traffic signal controller (BP) that does not require routing rates, it requires only aggregated queue lengths estimation (without direction information) and loop detectors at the stop line for each possible direction. A theoretical result on the Lyapunov drift in heavy load conditions under BP control is provided and tends to indicate that BP should have good stability properties. Simulations confirm this and show that BP stabilizes the queuing network in a significant part of the capacity region.Comment: accepted for presentation at IFAC 2014, 6 pages. arXiv admin note: text overlap with arXiv:1309.648

Muscle as a meta-material operating near a critical point

Passive mechanical response of skeletal muscles at fast time scales is dominated by long range interactions inducing cooperative behavior without breaking the detailed balance. This leads to such unusual "material properties" as negative equilibrium stiffness and different behavior in force and displacement controlled loading conditions. Our fitting of experimental data suggests that "muscle material" is finely tuned to perform close to a critical point which explains large fluctuations observed in muscles close to the stall force.Comment: Accepted for publication in Physical Review Letter

Null controllability of the 1D heat equation using flatness

We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach

Self-excited vibrations in turning: cutting moment analysis

This work aims at analysing the moment effects at the tool tip point and at the central axis, in the framework of a turning process. A testing device in turning, including a six-component dynamometer, is used to measure the complete torsor of the cutting actions in the case of self-excited vibrations. Many results are obtained regarding the mechanical actions torsor. A confrontation of the moment components at the tool tip and at the central axis is carried out. It clearly appears that analysing moments at the central axis avoids the disturbances induced by the transport of the moment of the mechanical actions resultant at the tool tip point. For instance, the order relation between the components of the forces is single. Furthermore, the order relation between the moments components expressed at the tool tip point is also single and the same one. But at the central axis, two different order relations regarding moments are conceivable. A modification in the rolling moment localization in the (y, z) tool plan is associated to these two order relations. Thus, the moments components at the central axis are particularly sensitive at the disturbances of machining, here the self-excited vibrations.Comment: 8 page

Semantic A-translation and Super-consistency entail Classical Cut Elimination

We show that if a theory R defined by a rewrite system is super-consistent, the classical sequent calculus modulo R enjoys the cut elimination property, which was an open question. For such theories it was already known that proofs strongly normalize in natural deduction modulo R, and that cut elimination holds in the intuitionistic sequent calculus modulo R. We first define a syntactic and a semantic version of Friedman's A-translation, showing that it preserves the structure of pseudo-Heyting algebra, our semantic framework. Then we relate the interpretation of a theory in the A-translated algebra and its A-translation in the original algebra. This allows to show the stability of the super-consistency criterion and the cut elimination theorem

Does foreign environmental policy influence domestic innovation? Evidence from the wind industry

This paper examines the relative influence of domestic and foreign renewable energy policies on innovation activity in wind power using patent data from OECD countries from 1994 to 2005. We distinguish between the impact of demand-pull policies (e.g., guaranteed tariffs, investment and production tax credits), as reflected by wind power capacities installed annually, and technology-push policies (government support to R&D). We show that inventors respond to both domestic and foreign new capacities by increasing their innovation effort. However, the effect on innovation of the marginal wind turbine installed at home is 28 times stronger than that of the foreign marginal wind turbine. Unlike demand-pull policies, public R&D expenditures only affect domestic inventors. A simple calculation suggests that the marginal million dollars spent on R&D support generates 0.82 new inventions, whereas the same amount spent on the deployment of wind turbines induces, at best, 0.06 new inventions (0.03 locally and 0.03 abroad)

A physics-based life prediction methodology for thermal barrier coating systems

A novel mechanistic approach is proposed for the prediction of the life of thermal barrier coating (TBC) systems. The life prediction methodology is based on a criterion linked directly to the dominant failure mechanism. It relies on a statistical treatment of the TBC's morphological characteristics, non-destructive stress measurements and on a continuum mechanics framework to quantify the stresses that promote the nucleation and growth of microcracks within the TBC. The last of these accounts for the effects of TBC constituents' elasto-visco-plastic properties, the stiffening of the ceramic due to sintering and the oxidation at the interface between the thermally insulating yttria stabilized zirconia (YSZ) layer and the metallic bond coat. The mechanistic approach is used to investigate the effects on TBC life of the properties and morphology of the top YSZ coating, metallic low-pressure plasma sprayed bond coat and the thermally grown oxide. Its calibration is based on TBC damage inferred from non-destructive fluorescence measurements using piezo-spectroscopy and on the numerically predicted local TBC stresses responsible for the initiation of such damage. The potential applicability of the methodology to other types of TBC coatings and thermal loading conditions is also discussed