13,373 research outputs found
The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow
Every neuron is part of a network, exerting its function by transforming multiple spatiotemporal synaptic input patterns into a single spiking output. This function is specified by the particular shape and passive electrical properties of the neuronal membrane, and the composition and spatial distribution of ion channels across its processes. For a variety of physiological or pathological reasons, the intrinsic input/output function may change during a neuron’s lifetime. This process results in high variability in the peak specific conductance of ion channels in individual neurons. The mechanisms responsible for this variability are not well understood, although there are clear indications from experiment and modeling that degeneracy and correlation among multiple channels may be involved. Here, we studied this issue in biophysical models of hippocampal CA1 pyramidal neurons and interneurons. Using a unified data-driven simulation workflow and starting from a set of experimental recordings and morphological reconstructions obtained from rats, we built and analyzed several ensembles of morphologically and biophysically accurate single cell models with intrinsic electrophysiological properties consistent with experimental findings. The results suggest that the set of conductances expressed in any given hippocampal neuron may be considered as belonging to two groups: one subset is responsible for the major characteristics of the firing behavior in each population and the other responsible for a robust degeneracy. Analysis of the model neurons suggests several experimentally testable predictions related to the combination and relative proportion of the different conductances that should be expressed on the membrane of different types of neurons for them to fulfill their role in the hippocampus circuitry
Best Subset Selection via a Modern Optimization Lens
In the last twenty-five years (1990-2014), algorithmic advances in integer
optimization combined with hardware improvements have resulted in an
astonishing 200 billion factor speedup in solving Mixed Integer Optimization
(MIO) problems. We present a MIO approach for solving the classical best subset
selection problem of choosing out of features in linear regression
given observations. We develop a discrete extension of modern first order
continuous optimization methods to find high quality feasible solutions that we
use as warm starts to a MIO solver that finds provably optimal solutions. The
resulting algorithm (a) provides a solution with a guarantee on its
suboptimality even if we terminate the algorithm early, (b) can accommodate
side constraints on the coefficients of the linear regression and (c) extends
to finding best subset solutions for the least absolute deviation loss
function. Using a wide variety of synthetic and real datasets, we demonstrate
that our approach solves problems with in the 1000s and in the 100s in
minutes to provable optimality, and finds near optimal solutions for in the
100s and in the 1000s in minutes. We also establish via numerical
experiments that the MIO approach performs better than {\texttt {Lasso}} and
other popularly used sparse learning procedures, in terms of achieving sparse
solutions with good predictive power.Comment: This is a revised version (May, 2015) of the first submission in June
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Passive Aeroelastic Tailoring
The Passive Aeroelastic Tailoring (PAT) project was tasked with investigating novel methods to achieve passive aeroelastic tailoring on high aspect ratio wings. The goal of the project was to identify structural designs or topologies that can improve performance and/or reduce structural weight for high-aspect ratio wings. This project considered two unique approaches, which were pursued in parallel: through-thickness topology optimization and composite tow-steering
Filling in CMB map missing data using constrained Gaussian realizations
For analyzing maps of the cosmic microwave background sky, it is necessary to
mask out the region around the galactic equator where the parasitic foreground
emission is strongest as well as the brightest compact sources. Since many of
the analyses of the data, particularly those searching for non-Gaussianity of a
primordial origin, are most straightforwardly carried out on full-sky maps, it
is of great interest to develop efficient algorithms for filling in the missing
information in a plausible way. We explore practical algorithms for filling in
based on constrained Gaussian realizations. Although carrying out such
realizations is in principle straightforward, for finely pixelized maps as will
be required for the Planck analysis a direct brute force method is not
numerically tractable. We present some concrete solutions to this problem, both
on a spatially flat sky with periodic boundary conditions and on the pixelized
sphere. One approach is to solve the linear system with an appropriately
preconditioned conjugate gradient method. While this approach was successfully
implemented on a rectangular domain with periodic boundary conditions and
worked even for very wide masked regions, we found that the method failed on
the pixelized sphere for reasons that we explain here. We present an approach
that works for full-sky pixelized maps on the sphere involving a kernel-based
multi-resolution Laplace solver followed by a series of conjugate gradient
corrections near the boundary of the mask.Comment: 22 pages, 14 figures, minor changes, a few missing references adde
(Global) Optimization: Historical notes and recent developments
Recent developments in (Global) Optimization are surveyed in this paper. We collected and commented quite a large number of recent references which, in our opinion, well represent the vivacity, deepness, and width of scope of current computational approaches and theoretical results about nonconvex optimization problems. Before the presentation of the recent developments, which are subdivided into two parts related to heuristic and exact approaches, respectively, we briefly sketch the origin of the discipline and observe what, from the initial attempts, survived, what was not considered at all as well as a few approaches which have been recently rediscovered, mostly in connection with machine learning
Towards an experimental von Karman dynamo: numerical studies for an optimized design
Numerical studies of a kinematic dynamo based on von Karman type flows
between two counterrotating disks in a finite cylinder are reported. The flow
has been optimized using a water model experiment, varying the driving
impellers configuration. A solution leading to dynamo action for the mean flow
has been found. This solution may be achieved in VKS2, the new sodium
experiment to be performed in Cadarache, France. The optimization process is
described and discussed, then the effects of adding a stationary conducting
layer around the flow on the threshold, on the shape of the neutral mode and on
the magnetic energy balance are studied. Finally, the possible processes
involved into kinematic dynamo action in a von Karman flow are reviewed and
discussed. Among the possible processes we highlight the joint effect of the
boundary-layer radial velocity shear and of the Ohmic dissipation localized at
the flow/outer-shell boundary
Fast, Optimal, and Safe Motion Planning for Bipedal Robots
Bipedal robots have the potential to traverse a wide range of unstructured environments, which are otherwise inaccessible to wheeled vehicles.
Though roboticists have successfully constructed controllers for bipedal robots to walk over uneven terrain such as snow, sand, or even stairs, it has remained challenging to synthesize such controllers in an online fashion while guaranteeing their satisfactory performance.
This is primarily due to the lack of numerical method that can accommodate the non-smooth dynamics, high degrees of freedom, and underactuation that characterize bipedal robots.
This dissertation proposes and implements a family of numerical methods that begin to address these three challenges along three dimensions: optimality, safety, and computational speed.
First, this dissertation develops a convex relaxation-based approach to solve optimal control for hybrid systems without a priori knowledge of the optimal sequence of transition.
This is accomplished by formulating the problem in the space of relaxed controls, which gives rise to a linear program whose solution is proven to compute the globally optimal controller.
This conceptual program is solved using a sequence of semidefinite programs whose solutions are proven to converge from below to the true optimal solution of the original optimal control problem.
Moreover, a method to synthesize the optimal controller is developed.
Using an array of examples, the performance of this method is validated on problems with known solutions and also compared to a commercial solver.
Second, this dissertation constructs a method to generate safety-preserving controllers for a planar bipedal robot walking on flat ground by performing reachability analysis on simplified models under the assumption that the difference between the two models can be bounded.
Subsequently, this dissertation describes how this reachable set can be incorporated into a Model Predictive Control framework to select controllers that result in safe walking on the biped in an online fashion.
This method is validated on a 5-link planar model.
Third, this dissertation proposes a novel parallel algorithm capable of finding guaranteed optimal solutions to polynomial optimization problems up to pre-specified tolerances.
Formal proofs of bounds on the time and memory usage of such method are also given.
Such algorithm is implemented in parallel on GPUs and compared against state-of-the-art solvers on a group of benchmark examples.
An application of such method on a real-time trajectory-planning task of a mobile robot is also demonstrated.
Fourth, this dissertation constructs an online Model Predictive Control framework that guarantees safety of a 3D bipedal robot walking in a forest of randomly-placed obstacles.
Using numerical integration and interval arithmetic techniques, approximations to trajectories of the robot are constructed along with guaranteed bounds on the approximation error.
Safety constraints are derived using these error bounds and incorporated in a Model Predictive Control framework whose feasible solutions keep the robot from falling over and from running into obstacles.
To ensure that the bipedal robot is able to avoid falling for all time, a finite-time terminal constraint is added to the Model Predictive Control algorithm.
The performance of this method is implemented and compared against a naive Model Predictive Control method on a biped model with 20 degrees of freedom.
In summary, this dissertation presents four methods for control synthesis of bipedal robots with improvements in either optimality, safety guarantee, or computational speed.
Furthermore, the performance of all proposed methods are compared with existing methods in the field.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162880/1/pczhao_1.pd
Conformator: A Novel Method for the Generation of Conformer Ensembles
Computer-aided drug design methods such as docking, pharmacophore searching, 3D database searching, and the creation of 3D-QSAR models need conformational ensembles to handle the flexibility of small molecules. Here, we present Conformator, an accurate and effective knowledge-based algorithm for generating conformer ensembles. With 99.9% of all test molecules processed, Conformator stands out by its robustness with respect to input formats, molecular geometries, and the handling of macrocycles. With an extended set of rules for sampling torsion angles, a novel algorithm for macrocycle conformer generation, and a new clustering algorithm for the assembly of conformer ensembles, Conformator reaches a median minimum root-mean-square deviation (measured between protein-bound ligand conformations and ensembles of a maximum of 250 conformers) of 0.47 Ă… with no significant difference to the highest-ranked commercial algorithm OMEGA and significantly higher accuracy than seven free algorithms, including the RDKit DG algorithm. Conformator is freely available for noncommercial use and academic research.acceptedVersio
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