Typical performance of generalised vector channels

We introduce a general matrix formulation for multiuser channels and analyse the special cases of Multiple-Input Multiple-Output channels, channels with interference and relay arrays under LDPC coding using methods developed for the statistical mechanics of disordered systems. We use the replica method to provide results for the typical overlaps of the original and recovered messages and discuss their implications. The results obtained are consistent with belief propagation and density evolution results but also complement them giving additional insights into the information dynamics of these channels with unexpected effects in some cases.

Networking - a statistical physics perspective

Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications. © 2013 IOP Publishing Ltd.

From the physics of interacting polymers to optimizing routes on the London Underground

Optimizing paths on networks is crucial for many applications, ranging from subway traffic to Internet communication. Because global path optimization that takes account of all path choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing suboptimal solutions. We use the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path optimization problems and derive a simple, principled, generic, and distributed routing algorithm capable of considering all individual path choices simultaneously. We demonstrate the efficacy of the algorithm by applying it to: (i) random graphs resembling Internet overlay networks, (ii) travel on the London Underground network based on Oyster card data, and (iii ) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, that facilitate better understanding of the appropriate operational regimes and their limitations, which are difficult to obtain otherwise.

Random distributed feedback fibre lasers

The concept of random lasers exploiting multiple scattering of photons in an amplifying disordered medium in order to generate coherent light without a traditional laser resonator has attracted a great deal of attention in recent years. This research area lies at the interface of the fundamental theory of disordered systems and laser science. The idea was originally proposed in the context of astrophysics in the 1960s by V.S. Letokhov, who studied scattering with "negative absorption" of the interstellar molecular clouds. Research on random lasers has since developed into a mature experimental and theoretical field. A simple design of such lasers would be promising for potential applications. However, in traditional random lasers the properties of the output radiation are typically characterized by complex features in the spatial, spectral and time domains, making them less attractive than standard laser systems in terms of practical applications. Recently, an interesting and novel type of one-dimensional random laser that operates in a conventional telecommunication fibre without any pre-designed resonator mirrors-random distributed feedback fibre laser-was demonstrated. The positive feedback required for laser generation in random fibre lasers is provided by the Rayleigh scattering from the inhomogeneities of the refractive index that are naturally present in silica glass. In the proposed laser concept, the randomly backscattered light is amplified through the Raman effect, providing distributed gain over distances up to 100km. Although an effective reflection due to the Rayleigh scattering is extremely small (~0.1%), the lasing threshold may be exceeded when a sufficiently large distributed Raman gain is provided. Such a random distributed feedback fibre laser has a number of interesting and attractive features. The fibre waveguide geometry provides transverse confinement, and effectively one-dimensional random distributed feedback leads to the generation of a stationary near-Gaussian beam with a narrow spectrum. A random distributed feedback fibre laser has efficiency and performance that are comparable to and even exceed those of similar conventional fibre lasers. The key features of the generated radiation of random distributed feedback fibre lasers include: a stationary narrow-band continuous modeless spectrum that is free of mode competition, nonlinear power broadening, and an output beam with a Gaussian profile in the fundamental transverse mode (generated both in single mode and multi-mode fibres).This review presents the current status of research in the field of random fibre lasers and shows their potential and perspectives. We start with an introductory overview of conventional distributed feedback lasers and traditional random lasers to set the stage for discussion of random fibre lasers. We then present a theoretical analysis and experimental studies of various random fibre laser configurations, including widely tunable, multi-wavelength, narrow-band generation, and random fibre lasers operating in different spectral bands in the 1-1.6μm range. Then we discuss existing and future applications of random fibre lasers, including telecommunication and distributed long reach sensor systems. A theoretical description of random lasers is very challenging and is strongly linked with the theory of disordered systems and kinetic theory. We outline two key models governing the generation of random fibre lasers: the average power balance model and the nonlinear Schrödinger equation based model. Recently invented random distributed feedback fibre lasers represent a new and exciting field of research that brings together such diverse areas of science as laser physics, the theory of disordered systems, fibre optics and nonlinear science. Stable random generation in optical fibre opens up new possibilities for research on wave transport and localization in disordered media. We hope that this review will provide background information for research in various fields and will stimulate cross-disciplinary collaborations on random fibre lasers. © 2014 Elsevier B.V.

Bosonisation as The Hubbard-Stratonovich transformation

The problem of strongly correlated electrons in one dimension attracted attention of condensed matter physicists since early 50’s. After the seminal paper of Tomonaga [1] who suggested the first soluble model in 1950, there were essential achievements reflected in papers by Luttinger [2] (1963) and Mattis and Lieb [3] (1963). A considerable contribution to the understanding of generic properties of the 1D electron liquid has been made by Dzyaloshinskii and Larkin [4] (1973) and Efetov and Larkin [5] (1976). Despite the fact that the main features of the 1D electron liquid were captured and described by the end of 70’s, the investigators felt dissatisfied with the rigour of the theoretical description. The most famous example is the paper by Haldane [6] (1981) where the author developed the fundamentals of a modern bosonisation technique, known as the operator approach. This paper became famous because the author has rigourously shown how to construct the Fermi creation/anihilation operators out of the Bose ones. The most recent example of such a dissatisfaction is the review by von Delft and Schoeller [7] (1998) who revised the approach to the bosonisation and came up with what they called constructive bosonisation.

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Transport properties of one-dimensional, disordered two-band systems

We have studied the transport properties of disordered one-dimensional two-band systems. The model includes a narrow d band hybridised with an s band. The Landauer formula was used in the case of a very narrow d band or in the case of short chains. The results were compared with the localisation length of the wavefunctions calculated by the transfer matrix method, which allows the use of very lang chains, and an excellent agreement was obtained.

Measuring complexity in three-trophic level systems

This essay is a trial on measuring complexity in a three-trophic level system by using a convex function of the informational entropy. The complexity measure defined here is compatible with the fact that real complexity lies between ordered and disordered states. Applying this measure to the data collected for two three-trophic level systems some hints about their organization are obtained. (C) 2008 Elsevier B.V. All rights reserved.

Contribution of cholinergic systems to state-dependent modulation of respiratory control

Respiration is altered during different stages of the sleep-wake cycle. We review the contribution of cholinergic systems to this alteration, with particular reference to the role of muscarinic acetylcholine receptors (MAchRs) during rapid eye movement (REM) sleep. Available evidence demonstrates that MAchRs have potent excitatory effects on medullary respiratory neurones and respiratory motoneurones, and are likely to contribute to changes in central chemosensitive drive to the respiratory control system. These effects are likely to be most prominent during REM sleep, when cholinergic brainstem neurones show peak activity levels. It is possible that MAchR dysfunction is involved in sleep-disordered breathing, Such as obstructive sleep apnea. (C) 2002 Elsevier Science B.V. All rights reserved.

Perpendicular magnetic anisotropy in chemically disordered FePd-FeV(100) alloy thin films

We find that the use of V(100) buffer layers on MgO(001) substrates for the epitaxy of FePd binary alloys yields to the formation at intermediate and high deposition temperatures of a FePd¿FeV mixed phase due to strong V diffusion accompanied by a loss of layer continuity and strong increase of its mosaic spread. Contrary to what is usually found in this kind of systems, these mixed phase structures exhibit perpendicular magnetic anisotropy (PMA) which is not correlated with the presence of chemical order, almost totally absent in all the fabricated structures, even at deposition temperatures where it is usually obtained with other buffer layers. Thus the observed PMA can be ascribed to the V interdiffusion and the formation of a FeV alloy, being the global sample saturation magnetization also reduced.

Growth of unstable interfaces in disordered media

The effects of a disordered medium in the growth of unstable interfaces are studied by means of two local models with multiplicative and additive quenched disorder, respectively. For short times and large pushing the multiplicative quenched disorder is equivalent to a time-dependent noise. In this regime, the linear dispersion relation contains a destabilizing contribution introduced by the noise. For long times, the interface always gets pinned. We model the systematics of the pinned shapes by means of an effective nonlinear model. These results show good agreement with numerical simulations. For the additive noise we find numerically that a depinning transition occurs.

Disordered backgammon model

In this paper we consider an exactly solvable model that displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated with different relaxational time scales. Low-temperature relaxation takes place by partial equilibration of successive lower-energy modes. An adiabatic scaling solution, defined in terms of a threshold energy scale e*, is proposed. For such a solution, modes with energy ee* are equilibrated at the bath temperature, modes with ee* remain out of equilibrium, and relaxation occurs in the neighborhood of the threshold e~e*. The model is presented as a toy example to investigate the conditions related to the existence of an effective temperature in glassy systems and its possible dependence on the energy sector is probed by the corresponding observable.

Teacher attitudes and the emotionally-behaviourally disordered middle school student

Inclusionary practlces prescrlbe that children, regardless of exceptlonal1ty shall benefit from recelving educatlonal servlce 1n the context of the regular class setting. The resulting el1mlnatlon of separate speclal classes could be v1ewed as aneconom1c advantage. In po1nt of fact, many school boards and d1strlcts 1n both Canada and the Unlted States are movlng towards 1mplementatlon of lncluslonary practice, posslbly for the above stated reason. Regardless, 1ncluslon as It relates to the emot1onal1y/behav1ourally disordered youth in our school systems may not be successful. Regular education teachers may not be prepared professlonal1y or personally to deal wlth this very spec1al student populat1on. Th1s study focused on teacher attitude 1n thls regard. As welll poss1ble factors that may lead to successful 1nclusion of these students are examined. Of these, teacher exper1ence, educat10n spec1f1c to the d1sab111ty of emot1onal/behavloural dlsordered comb1ned w1th teacher self-percept1on of success appear to hold the greatest promise. In v1ew of these flndlngs, recommendations are made for professlonal pract1ce and future research d1rect1ons.

Teacher attitudes and the emotionally-behaviourally disordered middle school student

Inclusionary practices prescribe that chl1dren, regardless of exceptional1ty shall benef1t from receiv1ng educational serv1ce 1n the context of the regular class sett1ng. The result1ng el1minat1on of separate spec1al classes could be v1ewed as an econom1c advantage. In point of fact, many school boards and d1str1cts 1n both Canada and the United States are mov1ng towards 1mplementat1on of inclusionary practice, possibly for the above stated reason. Regardless, 1nclusion as 1t relates to the emot1onally/behav1ourally disordered youth in our school systems may not be successful. Regular educat ion teachers may not be prepared profess1onally or personally to deal w1th this very special student population. Th1s study focused on teacher attitude 1n this regard. As well, poss1ble factors that may lead to successful 1nclusion of these students are examined. Of these, teacher exper1ence, educat10n spec1f1c to the d1sab1l1ty of emot1onal/behavioural d1sordered comb1ned w1th teacher self-perception of success appear to hold the greatest promise. In view of these findings, recommendat1ons are made for professional pract1ce and future research d1rect1ons.

The exclusive use of integer-order spots for LEED-IV structure analysis of adsorption systems: p(2×2)-O on Ni{111}

Two different ways of performing low-energy electron diffraction (LEED) structure determinations for the p(2 x 2) structure of oxygen on Ni {111} are compared: a conventional LEED-IV structure analysis using integer and fractional-order IV-curves collected at normal incidence and an analysis using only integer-order IV-curves collected at three different angles of incidence. A clear discrimination between different adsorption sites can be achieved by the latter approach as well as the first and the best fit structures of both analyses are within each other's error bars (all less than 0.1 angstrom). The conventional analysis is more sensitive to the adsorbate coordinates and lateral parameters of the substrate atoms whereas the integer-order-based analysis is more sensitive to the vertical coordinates of substrate atoms. Adsorbate-related contributions to the intensities of integer-order diffraction spots are independent of the state of long-range order in the adsorbate layer. These results show, therefore, that for lattice-gas disordered adsorbate layers, for which only integer-order spots are observed, similar accuracy and reliability can be achieved as for ordered adsorbate layers, provided the data set is large enough.