Regeneration limit of classical Shannon capacity

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit -the upper bound of regeneration efficiency -is derived. © 2014 Macmillan Publishers Limited. All rights reserved.

Shannon capacity of nonlinear communication channels

The exponentially increasing demand on operational data rate has been met with technological advances in telecommunication systems such as advanced multilevel and multidimensional modulation formats, fast signal processing, and research into new different media for signal transmission. Since the current communication channels are essentially nonlinear, estimation of the Shannon capacity for modern nonlinear communication channels is required. This PhD research project has targeted the study of the capacity limits of different nonlinear communication channels with a view to enable a significant enhancement in the data rate of the currently deployed fiber networks. In the current study, a theoretical framework for calculating the Shannon capacity of nonlinear regenerative channels has been developed and illustrated on the example of the proposed here regenerative Fourier transform (RFT). Moreover, the maximum gain in Shannon capacity due to regeneration (that is, the Shannon capacity of a system with ideal regenerators – the upper bound on capacity for all regenerative schemes) is calculated analytically. Thus, we derived a regenerative limit to which the capacity of any regenerative system can be compared, as analogue of the seminal linear Shannon limit. A general optimization scheme (regenerative mapping) has been introduced and demonstrated on systems with different regenerative elements: phase sensitive amplifiers and the proposed here multilevel regenerative schemes: the regenerative Fourier transform and the coupled nonlinear loop mirror.

On Multiple Deletion Codes

In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes for t = 2;3;4;5 with lengths n ≤ 30. Some of these codes improve on earlier results by Hirschberg-Fereira and Swart-Fereira. Finally, we prove a recursive upper bound on L2(n;t) which is asymptotically worse than the best known bounds, but gives better estimates for small values of n.

Optimization of Rational Approximations by Continued Fractions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.

Design of nonlinear regenerative transmission systems with high capacity

We present the design of nonlinear regenerative communication channels that have capacity above the classical Shannon capacity of the linear additive white Gaussian noise channel. The upper bound for regeneration efficiency is found and the asymptotic behavior of the capacity in the saturation regime is derived. © 2013 IEEE.

Misrepresentations and flawed logic about the prevalence of false memories

Brewin and Andrews (2016) propose that just 15% of people, or even fewer, are susceptible to false childhood memories. If this figure were true, then false memories would still be a serious problem. But the figure is higher than 15%. False memories occur even after a few short and low-pressure interviews, and with each successive interview they become richer, more compelling, and more likely to occur. It is therefore dangerously misleading to claim that the scientific data provide an “upper bound” on susceptibility to memory errors. We also raise concerns about the peer review process.

Two-bit pattern analysis for quantitative information flow

Protecting confidential information from improper disclosure is a fundamental security goal. While encryption and access control are important tools for ensuring confidentiality, they cannot prevent an authorized system from leaking confidential information to its publicly observable outputs, whether inadvertently or maliciously. Hence, secure information flow aims to provide end-to-end control of information flow. Unfortunately, the traditionally-adopted policy of noninterference, which forbids all improper leakage, is often too restrictive. Theories of quantitative information flow address this issue by quantifying the amount of confidential information leaked by a system, with the goal of showing that it is intuitively "small" enough to be tolerated. Given such a theory, it is crucial to develop automated techniques for calculating the leakage in a system. ^ This dissertation is concerned with program analysis for calculating the maximum leakage, or capacity, of confidential information in the context of deterministic systems and under three proposed entropy measures of information leakage: Shannon entropy leakage, min-entropy leakage, and g-leakage. In this context, it turns out that calculating the maximum leakage of a program reduces to counting the number of possible outputs that it can produce. ^ The new approach introduced in this dissertation is to determine two-bit patterns, the relationships among pairs of bits in the output; for instance we might determine that two bits must be unequal. By counting the number of solutions to the two-bit patterns, we obtain an upper bound on the number of possible outputs. Hence, the maximum leakage can be bounded. We first describe a straightforward computation of the two-bit patterns using an automated prover. We then show a more efficient implementation that uses an implication graph to represent the two- bit patterns. It efficiently constructs the graph through the use of an automated prover, random executions, STP counterexamples, and deductive closure. The effectiveness of our techniques, both in terms of efficiency and accuracy, is shown through a number of case studies found in recent literature. ^

(Table 1) Comparisons of dynamic and static Young's moduli of basalt at DSDP Holes 69-504B, 70-504B and 83-504B

Compressional- and shear-wave velocity logs (Vp and Vs, respectively) that were run to a sub-basement depth of 1013 m (1287.5 m sub-bottom) in Hole 504B suggest the presence of Layer 2A and document the presence of layers 2B and 2C on the Costa Rica Rift. Layer 2A extends from the mudline to 225 m sub-basement and is characterized by compressional-wave velocities of 4.0 km/s or less. Layer 2B extends from 225 to 900 m and may be divided into two intervals: an upper level from 225 to 600 m in which Vp decreases slowly from 5.0 to 4.8 km/s and a lower level from 600 to about 900 m in which Vp increases slowly to 6.0 km/s. In Layer 2C, which was logged for about 100 m to a depth of 1 km, Vp and Vs appear to be constant at 6.0 and 3.2 km/s, respectively. This velocity structure is consistent with, but more detailed than the structure determined by the oblique seismic experiment in the same hole. Since laboratory measurements of the compressional- and shear-wave velocity of samples from Hole 504B at Pconfining = Pdifferential average 6.0 and 3.2 km/s respectively, and show only slight increases with depth, we conclude that the velocity structure of Layer 2 is controlled almost entirely by variations in porosity and that the crack porosity of Layer 2C approaches zero. A comparison between the compressional-wave velocities determined by logging and the formation porosities calculated from the results of the large-scale resistivity experiment using Archie's Law suggest that the velocity- porosity relation derived by Hyndman et al. (1984) for laboratory samples serves as an upper bound for Vp, and the noninteractive relation derived by Toksöz et al. (1976) for cracks with an aspect ratio a = 1/32 serves as a lower bound.

Beam division multiple access for massive MIMO downlink transmission

We study a multiuser multicarrier downlink communication system in which the base station (BS) employs a large number of antennas. By assuming frequency-division duplex operation, we provide a beam domain channel model as the number of BS antennas grows asymptotically large. With this model, we first derive a closed-form upper bound on the achievable ergodic sum-rate before developing necessary conditions to asymptotically maximize the upper bound, with only statistical channel state information at the BS. Inspired by these conditions, we propose a beam division multiple access (BDMA) transmission scheme, where the BS communicates with users via different beams. For BDMA transmission, we design user scheduling to select users within non-overlapping beams, work out an optimal pilot design under a minimum mean square error criterion, and provide optimal pilot sequences by utilizing the Zadoff-Chu sequences. The proposed BDMA scheme reduces significantly the pilot overhead, as well as, the processing complexity at transceivers. Simulations demonstrate the high spectral efficiency of BDMA transmission and the advantages in the bit error rate performance of the proposed pilot sequences.

MRI-based assessment of the pineal gland in a large population of children aged 0-5 years and comparison with pineoblastoma: part I, the solid gland.

INTRODUCTION: Differentiation between normal solid (non-cystic) pineal glands and pineal pathologies on brain MRI is difficult. The aim of this study was to assess the size of the solid pineal gland in children (0-5 years) and compare the findings with published pineoblastoma cases. METHODS: We retrospectively analyzed the size (width, height, planimetric area) of solid pineal glands in 184 non-retinoblastoma patients (73 female, 111 male) aged 0-5 years on MRI. The effect of age and gender on gland size was evaluated. Linear regression analysis was performed to analyze the relation between size and age. Ninety-nine percent prediction intervals around the mean were added to construct a normal size range per age, with the upper bound of the predictive interval as the parameter of interest as a cutoff for normalcy. RESULTS: There was no significant interaction of gender and age for all the three pineal gland parameters (width, height, and area). Linear regression analysis gave 99 % upper prediction bounds of 7.9, 4.8, and 25.4 mm(2), respectively, for width, height, and area. The slopes (size increase per month) of each parameter were 0.046, 0.023, and 0.202, respectively. Ninety-three percent (95 % CI 66-100 %) of asymptomatic solid pineoblastomas were larger in size than the 99 % upper bound. CONCLUSION: This study establishes norms for solid pineal gland size in non-retinoblastoma children aged 0-5 years. Knowledge of the size of the normal pineal gland is helpful for detection of pineal gland abnormalities, particularly pineoblastoma.

Jeux de policiers et voleurs, Modèles et applications

Les jeux de policiers et voleurs sont étudiés depuis une trentaine d’années en informatique et en mathématiques. Comme dans les jeux de poursuite en général, des poursuivants (les policiers) cherchent à capturer des évadés (les voleurs), cependant ici les joueurs agissent tour à tour et sont contraints de se déplacer sur une structure discrète. On suppose toujours que les joueurs connaissent les positions exactes de leurs opposants, autrement dit le jeu se déroule à information parfaite. La première définition d’un jeu de policiers-voleurs remonte à celle de Nowakowski et Winkler [39] et, indépendamment, Quilliot [46]. Cette première définition présente un jeu opposant un seul policier et un seul voleur avec des contraintes sur leurs vitesses de déplacement. Des extensions furent graduellement proposées telles que l’ajout de policiers et l’augmentation des vitesses de mouvement. En 2014, Bonato et MacGillivray [6] proposèrent une généralisation des jeux de policiers-voleurs pour permettre l’étude de ceux-ci dans leur globalité. Cependant, leur modèle ne couvre aucunement les jeux possédant des composantes stochastiques tels que ceux dans lesquels les voleurs peuvent bouger de manière aléatoire. Dans ce mémoire est donc présenté un nouveau modèle incluant des aspects stochastiques. En second lieu, on présente dans ce mémoire une application concrète de l’utilisation de ces jeux sous la forme d’une méthode de résolution d’un problème provenant de la théorie de la recherche. Alors que les jeux de policiers et voleurs utilisent l’hypothèse de l’information parfaite, les problèmes de recherches ne peuvent faire cette supposition. Il appert cependant que le jeu de policiers et voleurs peut être analysé comme une relaxation de contraintes d’un problème de recherche. Ce nouvel angle de vue est exploité pour la conception d’une borne supérieure sur la fonction objectif d’un problème de recherche pouvant être mise à contribution dans une méthode dite de branch and bound.

On MDS convolutional codes over Z_p^r

Maximum distance separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in Oued and Sole (IEEE Trans Inf Theory 59(11):7305–7313, 2013) via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr from a new perspective. We introduce the notions of p-standard form and r-optimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over Zpr for any given set of parameters.

Numerical estimation of Carbonate properties using a digital rock physics workflow

Digital rock physics combines modern imaging with advanced numerical simulations to analyze the physical properties of rocks -- In this paper we suggest a special segmentation procedure which is applied to a carbonate rock from Switzerland -- Starting point is a CTscan of a specimen of Hauptmuschelkalk -- The first step applied to the raw image data is a nonlocal mean filter -- We then apply different thresholds to identify pores and solid phases -- Because we are aware of a nonneglectable amount of unresolved microporosity we also define intermediate phases -- Based on this segmentation determine porositydependent values for the pwave velocity and for the permeability -- The porosity measured in the laboratory is then used to compare our numerical data with experimental data -- We observe a good agreement -- Future work includes an analytic validation to the numerical results of the pwave velocity upper bound, employing different filters for the image segmentation and using data with higher resolution

Numerical enclosures of the optimal cost of the Kantorovitch’s mass transportation problem

International audience