Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the locations of stationary points of a nonparametric function, which also produces an estimate of the function. We use Gaussian processes as a flexible prior for the underlying function and impose derivative constraints to control the function's shape via conditioning. We develop an inferential strategy that intentionally restricts estimation to the case of at least one stationary point, bypassing possible mis-specifications in the number of stationary points and avoiding the varying dimension problem that often brings in computational complexity. We illustrate the proposed methods using simulations and then apply the method to the estimation of event-related potentials derived from electroencephalography (EEG) signals. We show how the proposed method automatically identifies characteristic components and their latencies at the individual level, which avoids the excessive averaging across subjects that is routinely done in the field to obtain smooth curves. By applying this approach to EEG data collected from younger and older adults during a speech perception task, we are able to demonstrate how the time course of speech perception processes changes with age.
- Award ID(s):
- 1634133
- NSF-PAR ID:
- 10109562
- Date Published:
- Journal Name:
- Queueing systems
- Volume:
- 92
- ISSN:
- 0257-0130
- Page Range / eLocation ID:
- 47-81
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This data set for the manuscript entitled "Design of Peptides that Fold and Self-Assemble on Graphite" includes all files needed to run and analyze the simulations described in the this manuscript in the molecular dynamics software NAMD, as well as the output of the simulations. The files are organized into directories corresponding to the figures of the main text and supporting information. They include molecular model structure files (NAMD psf or Amber prmtop format), force field parameter files (in CHARMM format), initial atomic coordinates (pdb format), NAMD configuration files, Colvars configuration files, NAMD log files, and NAMD output including restart files (in binary NAMD format) and trajectories in dcd format (downsampled to 10 ns per frame). Analysis is controlled by shell scripts (Bash-compatible) that call VMD Tcl scripts or python scripts. These scripts and their output are also included.
Version: 2.0
Changes versus version 1.0 are the addition of the free energy of folding, adsorption, and pairing calculations (Sim_Figure-7) and shifting of the figure numbers to accommodate this addition.
Conventions Used in These Files
===============================Structure Files
----------------
- graph_*.psf or sol_*.psf (original NAMD (XPLOR?) format psf file including atom details (type, charge, mass), as well as definitions of bonds, angles, dihedrals, and impropers for each dipeptide.)- graph_*.pdb or sol_*.pdb (initial coordinates before equilibration)
- repart_*.psf (same as the above psf files, but the masses of non-water hydrogen atoms have been repartitioned by VMD script repartitionMass.tcl)
- freeTop_*.pdb (same as the above pdb files, but the carbons of the lower graphene layer have been placed at a single z value and marked for restraints in NAMD)
- amber_*.prmtop (combined topology and parameter files for Amber force field simulations)
- repart_amber_*.prmtop (same as the above prmtop files, but the masses of non-water hydrogen atoms have been repartitioned by ParmEd)Force Field Parameters
----------------------
CHARMM format parameter files:
- par_all36m_prot.prm (CHARMM36m FF for proteins)
- par_all36_cgenff_no_nbfix.prm (CGenFF v4.4 for graphene) The NBFIX parameters are commented out since they are only needed for aromatic halogens and we use only the CG2R61 type for graphene.
- toppar_water_ions_prot_cgenff.str (CHARMM water and ions with NBFIX parameters needed for protein and CGenFF included and others commented out)Template NAMD Configuration Files
---------------------------------
These contain the most commonly used simulation parameters. They are called by the other NAMD configuration files (which are in the namd/ subdirectory):
- template_min.namd (minimization)
- template_eq.namd (NPT equilibration with lower graphene fixed)
- template_abf.namd (for adaptive biasing force)Minimization
-------------
- namd/min_*.0.namdEquilibration
-------------
- namd/eq_*.0.namdAdaptive biasing force calculations
-----------------------------------
- namd/eabfZRest7_graph_chp1404.0.namd
- namd/eabfZRest7_graph_chp1404.1.namd (continuation of eabfZRest7_graph_chp1404.0.namd)Log Files
---------
For each NAMD configuration file given in the last two sections, there is a log file with the same prefix, which gives the text output of NAMD. For instance, the output of namd/eabfZRest7_graph_chp1404.0.namd is eabfZRest7_graph_chp1404.0.log.Simulation Output
-----------------
The simulation output files (which match the names of the NAMD configuration files) are in the output/ directory. Files with the extensions .coor, .vel, and .xsc are coordinates in NAMD binary format, velocities in NAMD binary format, and extended system information (including cell size) in text format. Files with the extension .dcd give the trajectory of the atomic coorinates over time (and also include system cell information). Due to storage limitations, large DCD files have been omitted or replaced with new DCD files having the prefix stride50_ including only every 50 frames. The time between frames in these files is 50 * 50000 steps/frame * 4 fs/step = 10 ns. The system cell trajectory is also included for the NPT runs are output/eq_*.xst.Scripts
-------
Files with the .sh extension can be found throughout. These usually provide the highest level control for submission of simulations and analysis. Look to these as a guide to what is happening. If there are scripts with step1_*.sh and step2_*.sh, they are intended to be run in order, with step1_*.sh first.
CONTENTS
========The directory contents are as follows. The directories Sim_Figure-1 and Sim_Figure-8 include README.txt files that describe the files and naming conventions used throughout this data set.
Sim_Figure-1: Simulations of N-acetylated C-amidated amino acids (Ac-X-NHMe) at the graphite–water interface.
Sim_Figure-2: Simulations of different peptide designs (including acyclic, disulfide cyclized, and N-to-C cyclized) at the graphite–water interface.
Sim_Figure-3: MM-GBSA calculations of different peptide sequences for a folded conformation and 5 misfolded/unfolded conformations.
Sim_Figure-4: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.
Sim_Figure-5: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 295 K.
Sim_Figure-5_replica: Temperature replica exchange molecular dynamics simulations for the peptide cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) with 20 replicas for temperatures from 295 to 454 K.
Sim_Figure-6: Simulation of the peptide molecule cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) in free solution (no graphite).
Sim_Figure-7: Free energy calculations for folding, adsorption, and pairing for the peptide CHP1404 (sequence: cyc(GTGSGTG-GPGG-GCGTGTG-SGPG)). For folding, we calculate the PMF as function of RMSD by replica-exchange umbrella sampling (in the subdirectory Folding_CHP1404_Graphene/). We make the same calculation in solution, which required 3 seperate replica-exchange umbrella sampling calculations (in the subdirectory Folding_CHP1404_Solution/). Both PMF of RMSD calculations for the scrambled peptide are in Folding_scram1404/. For adsorption, calculation of the PMF for the orientational restraints and the calculation of the PMF along z (the distance between the graphene sheet and the center of mass of the peptide) are in Adsorption_CHP1404/ and Adsorption_scram1404/. The actual calculation of the free energy is done by a shell script ("doRestraintEnergyError.sh") in the 1_free_energy/ subsubdirectory. Processing of the PMFs must be done first in the 0_pmf/ subsubdirectory. Finally, files for free energy calculations of pair formation for CHP1404 are found in the Pair/ subdirectory.
Sim_Figure-8: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) where the peptides are far above the graphene–water interface in the initial configuration.
Sim_Figure-9: Two replicates of a simulation of nine peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.
Sim_Figure-9_scrambled: Two replicates of a simulation of nine peptide molecules with the control sequence cyc(GGTPTTGGGGGGSGGPSGTGGC) at the graphite–water interface at 370 K.
Sim_Figure-10: Adaptive biasing for calculation of the free energy of the folded peptide as a function of the angle between its long axis and the zigzag directions of the underlying graphene sheet.
This material is based upon work supported by the US National Science Foundation under grant no. DMR-1945589. A majority of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CHE-1726332, CNS-1006860, EPS-1006860, and EPS-0919443. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562, through allocation BIO200030. -
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Abstract We develop a new market‐making model, from the ground up, which is tailored toward high‐frequency trading under a limit order book (LOB), based on the well‐known classification of order types in market microstructure. Our flexible framework allows arbitrary order volume, price jump, and bid‐ask spread distributions as well as the use of market orders. It also honors the consistency of price movements upon arrivals of different order types. For example, it is apparent that prices should never go down on buy market orders. In addition, it respects the price‐time priority of LOB. In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov (Quantitative Finance, 8, 217, 2008) market‐making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order book features. The Hamilton‐Jacobi‐Bellman quasi‐variational inequality (HJBQVI) associated with the control problem can be solved numerically via finite‐difference method. We illustrate our optimal trading strategy with a full numerical analysis, calibrated to the order book statistics of a popular exchanged‐traded fund (ETF). Our simulation shows that the profit of market‐making can be severely overstated under LOBs with inconsistent price movements.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/doi/10.1007/s11134-019-09612-3
