Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Ist Religion schlecht für Frauen? Empirische Erkenntnisse zum Zusammenhang zwischen öffentlichen Religionen und den Menschenrechten der Frau

Religion is a dynamic concept. It can be a means of supporting masculinist power structures as well as a means for challenging established gender hierarchies. This article therefore suggests the proposition that it is not religion as such constituting a problem for the human rights of women but the privileging of patriarchal interpretations of religion and the marginalization of progressive interpretations in many contexts, respectively. From an empirical perspective, thus, the question of the concrete conditions contributing to the ability of conservative religious actors to enforce their patriarchal views in politics and society arises. This article consults existing empirical studies on predominantly Christian democracies and Muslim societies to find answers to this question. It discusses the impact that the institutional relations between the state and religion, the significance of religion in the political party system as well as the confessional composition and the strength of religiosity in a society have on the human rights of women. The article, moreover, deals with the effect of democracy and certain rights on the promotion of women's rights in religious contexts. It demonstrates the requirement of and provides suggestions for further empirical research in this area.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

Common priors for generalized type spaces

The notion of common prior is well-understood and widely-used in the incomplete information games literature. For ordinary type spaces the common prior is de�fined. Pint�er and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for �nite belief hierarchies, unawareness among others. In this paper we de�ne the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light.

Every hierarchy of beliefs is a type

When modeling game situations of incomplete information one usually considers the players’ hierarchies of beliefs, a source of all sorts of complications. Harsányi (1967-68)’s idea henceforth referred to as the ”Harsányi program” is that hierarchies of beliefs can be replaced by ”types”. The types constitute the ”type space”. In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.

Generalized type spaces

Ordinary type spaces (Heifetz and Samet, 1998) are essential ingredients of incomplete information games. With ordinary type spaces one can grab the notions of beliefs, belief hierarchies and common prior etc. However, ordinary type spaces cannot handle the notions of finite belief hierarchy and unawareness among others. In this paper we consider a generalization of ordinary type spaces, and introduce the so called generalized type spaces which can grab all notions ordinary type spaces can and more, finite belief hierarchies and unawareness among others. We also demonstrate that the universal generalized type space exists.

Common priors for generalized type spaces

The notion of common prior is well-understood and widely-used in the incomplete information games literature. For ordinary type spaces the common prior is defined. Pinter and Udvari (2011) introduce the notion of generalized type space. Generalized type spaces are models for various bonded rationality issues, for nite belief hierarchies, unawareness among others. In this paper we dene the notion of common prior for generalized types spaces. Our results are as follows: the generalization (1) suggests a new form of common prior for ordinary type spaces, (2) shows some quantum game theoretic results (Brandenburger and La Mura, 2011) in new light.

A new epistemic model

Meier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an infinitary language is used for the beliefs. In this paper we propose an epistemic model to fix the inconsistency above. We show that in this new model the universal knowledgebelief space exists, is complete and encompasses all belief hierarchies. Moreover, by examples we demonstrate that in this model the players can agree to disagree Aumann (1976)'s result does not hold, and Aumann and Brandenburger (1995)'s conditions are not sufficient for Nash equilibrium. However, we show that if we substitute selfevidence (Osborne and Rubinstein, 1994) for common knowledge, then we get at that both Aumann (1976)'s and Aumann and Brandenburger (1995)'s results hold.

Lexicographic allocations and extreme core payoffs: the case of assignment games

We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We first investigate the general relationship between these allocations and obtain two hierarchies on the class of balanced games. Secondly, we focus on assignment games and sharpen some of these general relationship. Our main result is the coincidence of the sets of lemarals (vectors of lexicographic maxima over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and extreme core points. As byproducts, we show that, similarly to the core and the coalitionally rational payoff set, also the dual coalitionally rational payoff set of an assignment game is determined by the individual and mixed-pair coalitions, and present an efficient and elementary way to compute these basic dual coalitional values. This provides a way to compute the Alexia value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game.

The role of disturbance and resource availability in structuring plant communities

Disturbances alter competitive hierarchies by reducing populations and altering resource regimes. The interaction between disturbance and resource availability may strongly influence the structure of plant communities, as observed in the recolonization of seagrass beds in outer Florida Bay that were denuded by sea-urchin overgrazing. There is no consensus concerning the interaction between disturbance and resource availability on competition intensity (CI). On the other hand, species diversity is dependent on both factors. Peaks in species diversity have been observed to occur when both resource availability and disturbance intensity are high, thus implying that CI is low. Based on this supposition of previous models, I presented the resource-disturbance hypothesis as a graphical model to make predictions of CI as a function of both disturbance intensity and the availability of a limiting resource. The predictions of this model were tested in two experiments within a seagrass community in south Florida, in which transplants of Halodule wrightii were placed into near-monocultures of Syringodium filiforme in a full-factorial array. In the first experiment, two measures of relative CI were calculated based on the changes in the short-shoot number (SS) and of rhizome length (RHL) on the transplants. Both light and disturbance were identified as important factors, though the interaction between light * disturbance was not significant. Relative CISS ranged between 0.2 and 1.0 for the high light and high disturbance treatments and the relative CIRHL < 0 for the same treatments, though results were not significantly different due to high variability and low sample size. These results, including a contour schematic using six data points from the different treatment combinations, preliminarily suggests that the resource-disturbance hypothesis may be used may be used as a next step in developing our understanding of the mechanisms involved in structuring plant communities. Furthermore, the focus of the model is on the outcome of CI, which may be a useful predictor of changes in species diversity. Further study is needed to confirm the results of this study and validate the usefulness of this model in other systems. ^

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

A educação básica na região metropolitana de Natal: uma análise da qualidade educativa e sua relação com o contexto familiar dos alunos

This dissertation aimed to investigate the formal learning process of children and teenagers through elementary education and, mainly, the support of family on domestic school activities as a step in the teaching-learning process. The student's family, with its cultural capital, provides an assistance which was the bias of the essay analyzes presented on this paper, using a spatial area of public elementary schools of the municipalities of the Natal metropolitan region. Such frame of Natal metropolis has been justified by the recent review of their basic education, taken by the Brazilian Ministry of Education, diagnosed in 2011, only 1% of students were in a adequate mathematics learning stage. While 62% were considered in a critical stage in this discipline. Given this issue, this dissertation offers a theoretical analysis about inherited and acquired within the family cultural capital, mainly focusing in the distances between the cultural level of the student's family and the defendant by the school. Then, presents the fundamental aspects of the issue on the urban phenomenon, focusing on social hierarchies and structures of city spaces that express differentiation, segmentation and socio-spatial segregation, and social exclusion. The emphasis on inequalities points to the development of an urban ethos, through formal schooling, which develops from social singularities. To theoretically develop the theme of Cultural Capital Family, this study sought to operationalize the concept through the interpretation of the phenomenon studied by a logical validation work hypotheses. The operation concepts systemically transformed into statistical indicators in order to measure the impact of individual, social and cultural characteristics of students elements. Finally, this dissertation found that the components evaluated, family cultural capital and housing conditions, can influence the development of skills and competencies of students in the educational sphere

Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Beyond the Convent Walls: The Local and Japan-wide Activities of Daihongan’s Nuns in the Early Modern Period (c. 1550–1868)

This dissertation examines the social and financial activities of Buddhist nuns to demonstrate how and why they deployed Buddhist doctrines, rituals, legends, and material culture to interact with society outside the convent. By examining the activities of the nuns of the Daihongan convent (one of the two administrative heads of the popular pilgrimage temple, Zenkōji) in Japan’s early modern period (roughly 1550 to 1868) as documented in the convent’s rich archival sources, I shed further light on the oft-overlooked political and financial activities of nuns, illustrate how Buddhist institutions interacted with the laity, provide further nuance to the discussion of how Buddhist women navigated patriarchal sectarian and secular hierarchies, and, within the field of Japanese history, give voice to women who were active outside of the household unit around which early modern Japanese society was organized.

Zenkōji temple, surrounded by the mountains of Nagano, has been one of Japan’s most popular pilgrimage sites since the medieval period. The abbesses of Daihongan, one Zenkōji’s main sub-temples, traveled widely to maintain connections with elite and common laypeople, participated in frequent country-wide displays of Zenkōji’s icon, and oversaw the creation of branch temples in Edo (now Tokyo), Osaka, Echigo (now Niigata), and Shinano (now Nagano). The abbesses of Daihongan were one of only a few women to hold the imperially sanctioned title of eminent person (shōnin 上人) and to wear purple robes. While this means that this Pure Land convent was in some ways not representative of all convents in early modern Japan, Daihongan’s position is particularly instructive because the existence of nuns and monks in a single temple complex allows us to see in detail how monastics of both genders interacted in close quarters.

This work draws heavily from the convent’s archival materials, which I used as a guide in framing my dissertation chapters. In the Introduction I discuss previous works on women in Buddhism. In Chapter 1, I briefly discuss the convent’s history and its place within the Zenkōji temple complex. In Chapter 2, I examine the convent’s regular economic bases and its expenditures. In Chapter 3, I highlight Daihongan’s branch temples and discuss the ways that they acted as nodes in a network connecting people in various areas to Daihongan and Zenkōji, thus demonstrating how a rural religious center extended its sphere of influence in urban settings. In Chapter 4, I discuss the nuns’ travels throughout the country to generate new and maintain old connections with the imperial court in Kyoto, confraternities in Osaka, influential women in the shogun’s castle, and commoners in Edo. In Chapter 5, I examine the convent’s reliance upon irregular means of income such as patronage, temple lotteries, loans, and displays of treasures, and how these were needed to balance irregular expenditures such as travel and the maintenance or reconstruction of temple buildings. Throughout the dissertation I describe Daihongan’s inner social structure comprised of abbesses, nuns, and administrators, and its local emplacement within Zenkōji and Zenkōji’s temple lands.

Exploring these themes sheds light on the lives of Japanese Buddhist nuns in this period. While the tensions between freedom and agency on the one hand and obligations to patrons, subordination to monks, or gender- and status-based restrictions on the other are important, and I discuss them in my work, my primary focus is on the nuns’ activities and lives. Doing so demonstrates that nuns were central figures in ever-changing economic and social networks as they made and maintained connections with the outside world through Buddhist practices and through precedents set centuries before. This research contributes to our understanding of nuns in Japan’s early modern period and will participate in and shape debates on the roles of women in patriarchal religious hierarchies.