58 research outputs found
About Homological Mirror Symmetry
The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is
discussed. We give first a self-contained study of derived categories and their
homological algebra, and later restrict to the bounded derived category of
schemes and ultimately Calabi--Yau manifolds, with particular emphasis on the
basics of the underlying sheaf theory, and the algebraic features therein.
Finally, we loosely discuss the lowest dimensional manifestations of
homological mirror symmetry, namely for elliptic curves and surfaces.
The present work is a sequel to the author's survey "Towards Homological
Mirror Symmetry" on the A-side of homological mirror symmetry.Comment: 138 pages, 2 figure
Sisyphus Effect in Pulse Coupled Excitatory Neural Networks with Spike-Timing Dependent Plasticity
The collective dynamics of excitatory pulse coupled neural networks with
spike timing dependent plasticity (STDP) is studied. Depending on the model
parameters stationary states characterized by High or Low Synchronization can
be observed. In particular, at the transition between these two regimes,
persistent irregular low frequency oscillations between strongly and weakly
synchronized states are observable, which can be identified as infraslow
oscillations with frequencies 0.02 - 0.03 Hz. Their emergence can be explained
in terms of the Sisyphus Effect, a mechanism caused by a continuous feedback
between the evolution of the coherent population activity and of the average
synaptic weight. Due to this effect, the synaptic weights have oscillating
equilibrium values, which prevents the neuronal population from relaxing into a
stationary macroscopic state.Comment: 18 pages, 24 figures, submitted to Physical Review
Towards Homological Mirror Symmetry
This is an expository article on the A-side of Kontsevich's Homological
Mirror Symmetry conjecture. We give first a self-contained study of
-categories and their homological algebra, and later restrict to
Fukaya categories, with particular emphasis on the basics of the underlying
Floer theory, and the geometric features therein. Finally, we place the theory
in the context of mirror symmetry, building towards its main predictions.Comment: 139 pages, 15 figures. Corrected a few minor typos, fixed an issue
with hyperlink
Pathways of mechanical unfolding of FnIII10: Low force intermediates
We study the mechanical unfolding pathways of the domain of
fibronectin by means of an Ising--like model, using both constant force and
constant velocity protocols. At high forces and high velocities our results are
consistent with experiments and previous computational studies. Moreover, the
simplicity of the model allows us to probe the biologically relevant low force
regime, where we predict the existence of two intermediates with very close
elongations. The unfolding pathway is characterized by stochastic transitions
between these two intermediates
Exact firing time statistics of neurons driven by discrete inhibitory noise
Neurons in the intact brain receive a continuous and irregular synaptic
bombardment from excitatory and inhibitory pre-synaptic neurons, which
determines the firing activity of the stimulated neuron. In order to
investigate the influence of inhibitory stimulation on the firing time
statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory
instantaneous post-synaptic potentials. In particular, we report exact results
for the firing rate, the coefficient of variation and the spike train spectrum
for various synaptic weight distributions. Our results are not limited to
stimulations of infinitesimal amplitude, but they apply as well to finite
amplitude post-synaptic potentials, thus being able to capture the effect of
rare and large spikes. The developed methods are able to reproduce also the
average firing properties of heterogeneous neuronal populations.Comment: 20 pages, 8 Figures, submitted to Scientific Report
Unfolding times for proteins in a force clamp
The escape process from the native valley for proteins subjected to a
constant stretching force is examined using a model for a Beta-barrel. For a
wide range of forces, the unfolding dynamics can be treated as one-dimensional
diffusion, parametrized in terms of the end-to-end distance. In particular, the
escape times can be evaluated as first passage times for a Brownian particle
moving on the protein free-energy landscape, using the Smoluchowski equation.
At strong forces, the unfolding process can be viewed as a diffusive drift away
from the native state, while at weak forces thermal activation is the relevant
mechanism. An escape-time analysis within this approach reveals a crossover
from an exponential to an inverse Gaussian escape-time distribution upon
passing from weak to strong forces. Moreover, a single expression valid at weak
and strong forces can be devised both for the average unfolding time as well as
for the corresponding variance. The analysis offers a possible explanation of
recent experimental findings for ddFLN4 and ubiquitin.Comment: 6 pages, 4 figures, submitted for pubblication to Physical Review
Letter
Reconstructing the free energy landscape of a mechanically unfolded model protein
The equilibrium free energy landscape of an off-lattice model protein as a
function of an internal (reaction) coordinate is reconstructed from
out-of-equilibrium mechanical unfolding manipulations. This task is
accomplished via two independent methods: by employing an extended version of
the Jarzynski equality (EJE) and the protein inherent structures (ISs). In a
range of temperatures around the ``folding transition'' we find a good
quantitative agreement between the free energies obtained via EJE and IS
approaches. This indicates that the two methodologies are consistent and able
to reproduce equilibrium properties of the examined system. Moreover, for the
studied model the structural transitions induced by pulling can be related to
thermodynamical aspects of folding
Free energy landscape of mechanically unfolded model proteins: extended Jarzinsky versus inherent structure reconstruction
The equilibrium free energy landscape of off-lattice model heteropolymers as
a function of an internal coordinate, namely the end-to-end distance, is
reconstructed from out-of-equilibrium steered molecular dynamics data. This
task is accomplished via two independent methods: by employing an extended
version of the Jarzynski equality (EJE) and the inherent structure (IS)
formalism. A comparison of the free energies estimated with these two schemes
with equilibrium results obtained via the umbrella sampling technique reveals a
good quantitative agreement among all the approaches in a range of temperatures
around the ``folding transition'' for the two examined sequences. In
particular, for the sequence with good foldability properties, the mechanically
induced structural transitions can be related to thermodynamical aspects of
folding. Moreover, for the same sequence the knowledge of the landscape profile
allows for a good estimation of the life times of the native configuration for
temperatures ranging from the folding to the collapse temperature. For the
random sequence, mechanical and thermal unfolding appear to follow different
paths along the landscape.Comment: Latex manuscript, 20 pages, 23 figures, submitted to Physical Review
Changing the mechanical unfolding pathway of FnIII10 by tuning the pulling strength
We investigate the mechanical unfolding of the tenth type III domain from
fibronectin, FnIII10, both at constant force and at constant pulling velocity,
by all-atom Monte Carlo simulations. We observe both apparent two-state
unfolding and several unfolding pathways involving one of three major, mutually
exclusive intermediate states. All the three major intermediates lack two of
seven native beta-strands, and share a quite similar extension. The unfolding
behavior is found to depend strongly on the pulling conditions. In particular,
we observe large variations in the relative frequencies of occurrence for the
intermediates. At low constant force or low constant velocity, all the three
major intermediates occur with a significant frequency. At high constant force
or high constant velocity, one of them, with the N- and C-terminal beta-strands
detached, dominates over the other two. Using the extended Jarzynski equality,
we also estimate the equilibrium free-energy landscape, calculated as a
function of chain extension. The application of a constant pulling force leads
to a free-energy profile with three major local minima. Two of these correspond
to the native and fully unfolded states, respectively, whereas the third one
can be associated with the major unfolding intermediates.Comment: 15 pages, 9 figure
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Exact firing time statistics of neurons driven by discrete inhibitory noise
Neurons in the intact brain receive a continuous and irregular synaptic
bombardment from excitatory and inhibitory pre-synaptic neurons, which
determines the firing activity of the stimulated neuron. In order to
investigate the influence of inhibitory stimulation on the firing time
statistics, we consider Leaky Integrate-and-Fire neurons subject to
inhibitory instantaneous post-synaptic potentials. In particular, we report
exact results for the firing rate, the coefficient of variation and the spike
train spectrum for various synaptic weight distributions. Our results are not
limited to stimulations of infinitesimal amplitude, but they apply as well to
finite amplitude post-synaptic potentials, thus being able to capture the
effect of rare and large spikes. The developed methods are able to reproduce
also the average firing properties of heterogeneous neuronal populations
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