The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

A guided heuristic approach to the MEG inverse problem.

There is general agreement within the scientific community in considering Biology as the science with more potential to develop in the XXI century. This is due to several reasons, but probably the most important one is the state of development of the rest of experimental and technological sciences. In this context, there are a very rich variety of mathematical tools, physical techniques and computer resources that permit to do biological experiments that were unbelievable only a few years ago. Biology is nowadays taking advantage of all these newly developed technologies, which are been applied to life sciences opening new research fields and helping to give new insights in many biological problems. Consequently, biologists have improved a lot their knowledge in many key areas as human function and human diseases. However there is one human organ that is still barely understood compared with the rest: The human brain. The understanding of the human brain is one of the main challenges of the XXI century. In this regard, it is considered a strategic research field for the European Union and the USA. Thus, there is a big interest in applying new experimental techniques for the study of brain function. Magnetoencephalography (MEG) is one of these novel techniques that are currently applied for mapping the brain activity1. This technique has important advantages compared to the metabolic-based brain imagining techniques like Functional Magneto Resonance Imaging2 (fMRI). The main advantage is that MEG has a higher time resolution than fMRI. Another benefit of MEG is that it is a patient friendly clinical technique. The measure is performed with a wireless set up and the patient is not exposed to any radiation. Although MEG is widely applied in clinical studies, there are still open issues regarding data analysis. The present work deals with the solution of the inverse problem in MEG, which is the most controversial and uncertain part of the analysis process3. This question is addressed using several variations of a new solving algorithm based in a heuristic method. The performance of those methods is analyzed by applying them to several test cases with known solutions and comparing those solutions with the ones provided by our methods.

Don't blame the economists. It is an inverse problem!

The seriousness of the current crisis urgently demands new economic thinking that breaks the austerity vs. deficit spending circle in economic policy. The core tenet of the paper is that the most important problems that natural and social science are facing today are inverse problems, and that a new approach that goes beyond optimization is necessary. The approach presented here is radical in the sense that it identifies the roots in key assumptions in economic theory such as optimal behavior and stability to provide an inverse thinking perspective to economic modeling, of use in economic and financial stability policy. The inverse problem provides a truly multidisciplinary platform where related problems from different disciplines can be studied under a common approach with comparable results.

Statistical mechanics approaches to granular media: between micromechanics and macromechanics

The mechanical behavior of granular materials has been traditionally approached through two theoretical and computational frameworks: macromechanics and micromechanics. Macromechanics focuses on continuum based models. In consequence it is assumed that the matter in the granular material is homogeneous and continuously distributed over its volume so that the smallest element cut from the body possesses the same physical properties as the body. In particular, it has some equivalent mechanical properties, represented by complex and non-linear constitutive relationships. Engineering problems are usually solved using computational methods such as FEM or FDM. On the other hand, micromechanics is the analysis of heterogeneous materials on the level of their individual constituents. In granular materials, if the properties of particles are known, a micromechanical approach can lead to a predictive response of the whole heterogeneous material. Two classes of numerical techniques can be differentiated: computational micromechanics, which consists on applying continuum mechanics on each of the phases of a representative volume element and then solving numerically the equations, and atomistic methods (DEM), which consist on applying rigid body dynamics together with interaction potentials to the particles. Statistical mechanics approaches arise between micro and macromechanics. It tries to state which the expected macroscopic properties of a granular system are, by starting from a micromechanical analysis of the features of the particles and the interactions. The main objective of this paper is to introduce this approach.

Optimum Design of Electromagnets for Magnetic Levitation of Transport Systems based on the Inverse Problem Solutions

Article is devoted to design of optimum electromagnets for magnetic levitation of transport systems. The method of electromagnets design based on the inverse problem solution of electrical equipment is offered. The method differs from known by introducing a stage of minimization the target functions providing the stated levitation force and magnetic induction in a gap, and also the mass of an electromagnet. Initial values of parameters are received, using approximate formulas of the theory of electric devices and electrical equipment. The example of realization of a method is given. The received results show its high efficiency at design. It is practical to use the offered method and the computer program realizing it as a part of system of the automated design of electric equipment for transport with a magnetic levitation.

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Many-body quantum dynamics of polarization squeezing in optical fibers

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fiber, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibers. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.

Statistical mechanics of mutual information maximization

An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker S. and Hinton G., Nature, 355 (1992) 161). By exploiting a formal analogy to supervised learning in parity machines, the theory of zero-temperature Gibbs learning for the unsupervised procedure is presented for the case that the networks are perceptrons and for the case of fully connected committees.

Statistical mechanics of typical set decoding

The performance of "typical set (pairs) decoding" for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding method, errors occur, either when the information transmission is corrupted by atypical noise, or when multiple typical sequences satisfy the parity check equation as provided by the received corrupted codeword. We show that the average error rate for the second type of error over a given code ensemble can be accurately evaluated using the replica method, including the sensitivity to message length. Our approach generally improves the existing analysis known in the information theory community, which was recently reintroduced in IEEE Trans. Inf. Theory 45, 399 (1999), and is believed to be the most accurate to date. © 2002 The American Physical Society.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

Statistical mechanics of broadcast channels using low-density parity-check codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

A verifiable solution to the MEG inverse problem

Magnetoencephalography (MEG) is a non-invasive brain imaging technique with the potential for very high temporal and spatial resolution of neuronal activity. The main stumbling block for the technique has been that the estimation of a neuronal current distribution, based on sensor data outside the head, is an inverse problem with an infinity of possible solutions. Many inversion techniques exist, all using different a-priori assumptions in order to reduce the number of possible solutions. Although all techniques can be thoroughly tested in simulation, implicit in the simulations are the experimenter's own assumptions about realistic brain function. To date, the only way to test the validity of inversions based on real MEG data has been through direct surgical validation, or through comparison with invasive primate data. In this work, we constructed a null hypothesis that the reconstruction of neuronal activity contains no information on the distribution of the cortical grey matter. To test this, we repeatedly compared rotated sections of grey matter with a beamformer estimate of neuronal activity to generate a distribution of mutual information values. The significance of the comparison between the un-rotated anatomical information and the electrical estimate was subsequently assessed against this distribution. We found that there was significant (P < 0.05) anatomical information contained in the beamformer images across a number of frequency bands. Based on the limited data presented here, we can say that the assumptions behind the beamformer algorithm are not unreasonable for the visual-motor task investigated.

Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

Inverse Problem for Fractional Diffusion Equation

MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30

Efficient algorithm for routing optimization via statistical mechanics

Many practical routing algorithms are heuristic, adhoc and centralized, rendering generic and optimal path configurations difficult to obtain. Here we study a scenario whereby selected nodes in a given network communicate with fixed routers and employ statistical physics methods to obtain optimal routing solutions subject to a generic cost. A distributive message-passing algorithm capable of optimizing the path configuration in real instances is devised, based on the analytical derivation, and is greatly simplified by expanding the cost function around the optimized flow. Good algorithmic convergence is observed in most of the parameter regimes. By applying the algorithm, we study and compare the pros and cons of balanced traffic configurations to that of consolidated traffic, which provides important implications to practical communication and transportation networks. Interesting macroscopic phenomena are observed from the optimized states as an interplay between the communication density and the cost functions used. © 2013 IEEE.