Threshold-induced phase transitions in perceptrons

Error rates of a Boolean perceptron with threshold and either spherical or Ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one-step replica symmetry breaking (RSB) treatment. For unbiased output distribution and non-zero stability of the patterns, we find a critical load, α p, above which two solutions to the saddlepoint equations appear; one with higher free energy and zero threshold and a dominant solution with non-zero threshold. We examine this second-order phase transition and the dependence of α p on the required pattern stability, κ, for both one-step RSB and replica symmetry (RS) in the spherical case and for one-step RSB in the Ising case.

Betwixt spaces: student accounts of turning point experiences in first year transitions

‘Not belonging’ is becoming a prevalent theme within accounts of the first-year student experience at university. In this study the notion of not belonging is extended by assuming a more active role for the idea of liminality in a student’s transition into the university environments of academic and student life. In doing so, the article suggests that the transition between one place (home) and another (university) can result in an ‘in-between-ness’ – a betwixt space. Through an interpretative methodology, the study explores how students begin to move from this betwixt space into feeling like fully-fledged members of university life. It is concluded that there is a wide range of turning points associated with the students’ betwixt transition, which shapes, alters or indeed accentuates the ways in which they make meaningful connections with university life. Moreover, transitional turning point experiences reveal a cast of characters and symbolic objects; capture contrasting motivations and evolving relationships; display multiple trajectories of interpersonal tensions and conflicts; highlight discontinuities as well as continuities; and together, simultaneously liberate and constrain the students’ transition into university life.

Nation, region and history in post-communist transitions:identity politics in Ukraine, 1991-2006

Since independence in 1991, issues of nation and identity have become highly debated topics in Ukraine. This monograph explores not only how national identity is being (re)constructed by the Ukrainian state, but also the processes by which it is negotiated through society. The central argument of this work is that too much attention, concerning identity in Ukraine, has focused on markers of ethnicity and language. Instead, the author advocates a regional approach, engaging with the issue of how Ukraine's regional differences affect nation-building processes. Following the tumultuous events of the 'Orange Revolution', the view of Ukraine as a country inherently 'divided' between 'East' and 'West' has (re)emerged to become a popular explanation for political events. The study outlines the necessity for academics, policymakers and indeed politicians to veer away from this simplistic 'West versus East' divide. The book advocates an analysis of Ukraine's unique brand of regionalism not in terms of divisions, but in terms of regional differences and diversity. The author deconstructs the concept of 'Eastern Ukraine' by focusing on three Ukrainian localities, all adjacent to the Ukrainian-Russian border. The study examines how individuals provide 'their' own understanding of the place of their region within the wider processes of nation building across Ukraine. In doing so, the book develops a 'regional' approach to the study of identity politics in Ukraine.

Phase transitions and memory effects in the dynamics of Boolean networks

The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible via commonly used approximations. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between Boolean networks and general Boolean formulas are identified and results common to both system types are highlighted. © 2012 Copyright Taylor and Francis Group, LLC.

Computing with noise: phase transitions in Boolean formulas

Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results on error rates, function depth, and sensitivity, and their dependence on the gate-type and noise model used are also obtained.

21-residue peptide's dynamics at and between elementary structural transitions

Elementary conformational changes of the backbone of a 21-residue peptide A5(A3RA)3A are studied using molecular dynamics simulations in explicit water. The processes of the conformational transitions and the regimes of stationary fluctuations between them are investigated using minimal perturbations of the system. The perturbations consist of a few degrees rotation of the velocity of one of the systems' atoms and keep the system on the same energy surface. It is found that (i) the system dynamics is insignificantly changed by the perturbations in the regimes between the transitions; (ii) it is very sensitive to the perturbations just before the transitions that prevents the peptide from making the transitions; and (iii) the perturbation of any atom of the system, including distant water molecules is equally effective in preventing the transition. The latter implies strongly collective dynamics of the peptide and water during the transitions.

Phase transitions in wave turbulence

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space. At the highest level reached, we observe a short-range positional and long-range orientational order (as in a hexatic phase). In other words, the more one pumps the system, the more ordered the system becomes. The phase transitions happen when the system is pumped by an instability term and does not occur when pumped by a random force. We thus demonstrate nonuniversality of an inverse-cascade turbulence with respect to the nature of small-scale forcing.