581 research outputs found
Helical Tubes in Crowded Environments
When placed in a crowded environment, a semi-flexible tube is forced to fold
so as to make a more compact shape. One compact shape that often arises in
nature is the tight helix, especially when the tube thickness is of comparable
size to the tube length. In this paper we use an excluded volume effect to
model the effects of crowding. This gives us a measure of compactness for
configurations of the tube, which we use to look at structures of the
semi-flexible tube that minimize the excluded volume. We focus most of our
attention on the helix and which helical geometries are most compact. We found
that helices of specific pitch to radius ratio 2.512 to be optimally compact.
This is the same geometry that minimizes the global curvature of the curve
defining the tube. We further investigate the effects of adding a bending
energy or multiple tubes to begin to explore the more complete space of
possible geometries a tube could form.Comment: 10 page
Superuniversality from disorder at two-dimensional topological phase transitions
We investigate the effects of quenched randomness on topological quantum
phase transitions in strongly interacting two-dimensional systems. We focus
first on transitions driven by the condensation of a subset of fractionalized
quasiparticles (`anyons') identified with `electric charge' excitations of a
phase with intrinsic topological order. All other anyons have nontrivial mutual
statistics with the condensed subset and hence become confined at the anyon
condensation transition. Using a combination of microscopically exact duality
transformations and asymptotically exact real-space renormalization group
techniques applied to these two-dimensional disordered gauge theories, we argue
that the resulting critical scaling behavior is `superuniversal' across a wide
range of such condensation transitions, and is controlled by the same
infinite-randomness fixed point as that of the 2D random transverse-field Ising
model. We validate this claim using large-scale quantum Monte Carlo simulations
that allow us to extract zero-temperature critical exponents and correlation
functions in (2+1)D disordered interacting systems. We discuss generalizations
of these results to a large class of ground-state and excited-state topological
transitions in systems with intrinsic topological order as well as those where
topological order is either protected or enriched by global symmetries. When
the underlying topological order and the symmetry group are Abelian, our
results provide prototypes for topological phase transitions between distinct
many-body localized phases.Comment: 33 pages, 35 figures; published versio
RELEASE: A High-level Paradigm for Reliable Large-scale Server Software
Erlang is a functional language with a much-emulated model for building reliable distributed systems. This paper outlines the RELEASE project, and describes the progress in the first six months. The project aim is to scale the Erlang’s radical concurrency-oriented programming paradigm to build reliable general-purpose software, such as server-based systems, on massively parallel machines. Currently Erlang has inherently scalable computation and reliability models, but in practice scalability is constrained by aspects of the language and virtual machine. We are working at three levels to address these challenges: evolving the Erlang virtual machine so that it can work effectively on large scale multicore systems; evolving the language to Scalable Distributed (SD) Erlang; developing a scalable Erlang infrastructure to integrate multiple, heterogeneous clusters. We are also developing state of the art tools that allow programmers to understand the behaviour of massively parallel SD Erlang programs. We will demonstrate the effectiveness of the RELEASE approach using demonstrators and two large case studies on a Blue Gene
Ground-state properties of tubelike flexible polymers
In this work we investigate structural properties of native states of a
simple model for short flexible homopolymers, where the steric influence of
monomeric side chains is effectively introduced by a thickness constraint. This
geometric constraint is implemented through the concept of the global radius of
curvature and affects the conformational topology of ground-state structures. A
systematic analysis allows for a thickness-dependent classification of the
dominant ground-state topologies. It turns out that helical structures,
strands, rings, and coils are natural, intrinsic geometries of such tubelike
objects
Education and articulation: Laclau and Mouffe’s radical democracy in school
This paper outlines a theory of radical democratic education by addressing a key concept in Laclau and Mouffe’s Hegemony and Socialist Strategy: articulation. Through their concept of articulation, Laclau and Mouffe attempt to liberate Gramsci’s theory of hegemony from Marxist economism, and adapt it to a political sphere inhabited by a plurality of struggles and agents none of which is predominant. However, while for Gramsci the political process of hegemony formation has an explicit educational dimension, Laclau and Mouffe ignore this dimension altogether. My discussion starts with elaborating the concept of articulation and analysing it in terms of three dimensions: performance, connection and transformation. I then address the role of education in Gramsci’s politics, in which the figure of the intellectual is central, and argue that radical democratic education requires renouncing that figure. In the final section, I offer a theory of such education, in which both teacher and students articulate their political differences and identities
New Developments in Quantum Algorithms
In this survey, we describe two recent developments in quantum algorithms.
The first new development is a quantum algorithm for evaluating a Boolean
formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This
provides quantum speedups for any problem that can be expressed via Boolean
formulas. This result can be also extended to span problems, a generalization
of Boolean formulas. This provides an optimal quantum algorithm for any Boolean
function in the black-box query model.
The second new development is a quantum algorithm for solving systems of
linear equations. In contrast with traditional algorithms that run in time
O(N^{2.37...}) where N is the size of the system, the quantum algorithm runs in
time O(\log^c N). It outputs a quantum state describing the solution of the
system.Comment: 11 pages, 1 figure, to appear as an invited survey talk at MFCS'201
How spiking neurons give rise to a temporal-feature map
A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit
from the nonlinearity
Democratization in a passive dendritic tree : an analytical investigation
One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius
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