A diagrammatic approach to study the information transfer in weakly non-linear channels

In a recent work we have introduced a novel approach to study the effect of weak non-linearities in the transfer function on the information transmitted by an analogue channel, by means of a perturbative diagrammatic expansion. We extend here the analysis to all orders in perturbation theory, which allows us to release any constraint concerning the magnitude of the expansion parameter and to establish the rules to calculate easily the contribution at any order. As an example we explicitly compute the information up to the second order in the non-linearity, in presence of random gaussian connectivities and in the limit when the output noise is not small. We analyze the first and second order contributions to the mutual information as a function of the non-linearity and of the number of output units. We believe that an extensive application of our method via the analysis of the different contributions at distinct orders might be able to fill a gap between well known analytical results obtained for linear channels and the non trivial treatments which are required to study highly non-linear channels.Comment: 17 pages, 3 figure

A replica free evaluation of the neuronal population information with mixed continuous and discrete stimuli: from the linear to the asymptotic regime

Recent studies have explored theoretically the ability of populations of neurons to carry information about a set of stimuli, both in the case of purely discrete or purely continuous stimuli, and in the case of multidimensional continuous angular and discrete correlates, in presence of additional quenched disorder in the distribution. An analytical expression for the mutual information has been obtained in the limit of large noise by means of the replica trick. Here we show that the same results can actually be obtained in most cases without the use of replicas, by means of a much simpler expansion of the logarithm. Fitting the theoretical model to real neuronal data, we show that the introduction of correlations in the quenched disorder improves the fit, suggesting a possible role of signal correlations-actually detected in real data- in a redundant code. We show that even in the more difficult analysis of the asymptotic regime, an explicit expression for the mutual information can be obtained without resorting to the replica trick despite the presence of quenched disorder, both with a gaussian and with a more realistic thresholded-gaussian model. When the stimuli are mixed continuous and discrete, we find that with both models the information seem to grow logarithmically to infinity with the number of neurons and with the inverse of the noise, even though the exact general dependence cannot be derived explicitly for the thresholded gaussian model. In the large noise limit lower values of information were obtained with the thresholded-gaussian model, for a fixed value of the noise and of the population size. On the contrary, in the asymptotic regime, with very low values of the noise, a lower information value is obtained with the gaussian model.Comment: 34 pages, 5 figure

Nanometer-scale Tomographic Reconstruction of 3D Electrostatic Potentials in GaAs/AlGaAs Core-Shell Nanowires

We report on the development of Electron Holographic Tomography towards a versatile potential measurement technique, overcoming several limitations, such as a limited tilt range, previously hampering a reproducible and accurate electrostatic potential reconstruction in three dimensions. Most notably, tomographic reconstruction is performed on optimally sampled polar grids taking into account symmetry and other spatial constraints of the nanostructure. Furthermore, holographic tilt series acquisition and alignment have been automated and adapted to three dimensions. We demonstrate 6 nm spatial and 0.2 V signal resolution by reconstructing various, previously hidden, potential details of a GaAs/AlGaAs core-shell nanowire. The improved tomographic reconstruction opens pathways towards the detection of minute potentials in nanostructures and an increase in speed and accuracy in related techniques such as X-ray tomography

Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of multi-dimensional continuous+discrete stimuli, for a finite population size and in the limit of large noise. Here, we extend the analysis to the case of two interconnected populations, where input units activate output ones via gaussian weights and a threshold linear transfer function. We evaluate the information carried by a population of M output units, again about continuous+discrete correlates. The mutual information is evaluated solving saddle point equations under the assumption of replica symmetry, a method which, by taking into account only the term linear in N of the input information, is equivalent to assuming the noise to be large. Within this limitation, we analyze the dependence of the information on the ratio M/N, on the selectivity of the input units and on the level of the output noise. We show analytically, and confirm numerically, that in the limit of a linear transfer function and of a small ratio between output and input noise, the output information approaches asymptotically the information carried in input. Finally, we show that the information loss in output does not depend much on the structure of the stimulus, whether purely continuous, purely discrete or mixed, but only on the position of the threshold nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure

An architecture to integrate IEC 61131-3 systems in an IEC 61499 distributed solution

The IEC 61499 standard has been developed to allow the modeling and design of distributed control systems, providing advanced concepts of software engineering (such as abstraction and encapsulation) to the world of control engineering. The introduction of this standard in already existing control environments poses challenges, since programs written using the widespread IEC 61131-3 programming standard cannot be directly executed in a fully IEC 61499 environment without reengineering effort. In order to solve this problem, this paper presents an architecture to integrate modules of the two standards, allowing the exploitation of the benefits of both. The proposed architecture is based on the coexistence of control software of the two standards. Modules written in one standard interact with some particular interfaces that encapsulate functionalities and information to be exchanged with the other standard. In particular, the architecture permits to utilize available run-times without modification, it allows the reuse of software modules, and it utilizes existing features of the standards. A methodology to integrate IEC 61131-3 modules in an IEC 61499 distributed solution based on such architecture is also developed, and it is described via a case study to prove feasibility and benefits. Experimental results demonstrate that the proposed solution does not add substantial load or delays to the system when compared to an IEC 61131-3 based solution. By acting on task period, it can achieve performances similar to an IEC 61499 solution

A Study on Secret Key Rate in Wideband Rice Channel

Standard cryptography is expected to poorly fit IoT applications and services, as IoT devices can hardly cope with the computational complexity often required to run encryption algorithms. In this framework, physical layer security is often claimed as an effective solution to enforce secrecy in IoT systems. It relies on wireless channel characteristics to provide a mechanism for secure communications, with or even without cryptography. Among the different possibilities, an interesting solution aims at exploiting the random-like nature of the wireless channel to let the legitimate users agree on a secret key, simultaneously limiting the eavesdropping threat thanks to the spatial decorrelation properties of the wireless channel. The actual reliability of the channel-based key generation process depends on several parameters, as the actual correlation between the channel samples gathered by the users and the noise always affecting the wireless communications. The sensitivity of the key generation process can be expressed by the secrecy key rate, which represents the maximum number of secret bits that can be achieved from each channel observation. In this work, the secrecy key rate value is computed by means of simulations carried out under different working conditions in order to investigate the impact of major channel parameters on the SKR values. In contrast to previous works, the secrecy key rate is computed under a line-of-sight wireless channel and considering different correlation levels between the legitimate users and the eavesdropper

Feasibility of laparoscopic portal vein ligation prior to major hepatectomy

AbstractBackground. Patients noted to have an inadequate future liver remnant on pre operative volumetric assessment are considered to be candidates for portal vein embolization (PVE). A subset of patients undergo laparoscopic intervention prior to PVE for staging purposes or to address the primary in Stage IV colon cancer. These patients usually undergo PVE as a subsequent additional procedure by the transhepatic route. The aim of this study was to assess the feasibility of portal vein ligation by the laparoscopic approach in suitable patients. Materials and methods. A retrospective review of a prospectively maintained database was performed to identify patients that underwent laparoscopic portal vein ligation (LPVL). The demographic, clinical, radiographic, operative and volumetric details were collected to determine the feasibility of portal vein ligation. Results. A total of nine patients underwent LPVL as part of a two stage procedure in preparation for subsequent major hepatectomy. With a median age of 67 yrs, the diagnoses included: colorectal metastasis (five patients), cholangiocarcinoma (three patients) and hepatocellular carcinoma (one patient). The ligation involved the right portal vein in all and was performed with silk ligature (seven patients) and clips (two patients). Volumetric data was available in six patients which showed a mean increase from 209.1 cc±97.76 to 495.83 cc±310.91 (increase by 181.5%) In two patients, inadequate hypertrophy mandated later embolization by percutaneous technique. Five patients underwent subsequent major hepatic resection as planned. The remaining four patients were noted to have progression of disease that precluded the planned procedure. There were no complications associated with LPVL. Conclusions. LPVL is feasible and can be safely performed. In a select group of patients, it may be considered as an alternative to subsequent embolization and thereby potentially absolve the need for an additional procedure with its attendant complications