763 research outputs found
Bayesian Optimization with Unknown Constraints
Recent work on Bayesian optimization has shown its effectiveness in global
optimization of difficult black-box objective functions. Many real-world
optimization problems of interest also have constraints which are unknown a
priori. In this paper, we study Bayesian optimization for constrained problems
in the general case that noise may be present in the constraint functions, and
the objective and constraints may be evaluated independently. We provide
motivating practical examples, and present a general framework to solve such
problems. We demonstrate the effectiveness of our approach on optimizing the
performance of online latent Dirichlet allocation subject to topic sparsity
constraints, tuning a neural network given test-time memory constraints, and
optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed
time, subject to passing standard convergence diagnostics.Comment: 14 pages, 3 figure
Attraction Between Like-Charged Walls: Short-Ranged Simulations Using Local Molecular Field Theory
Effective attraction between like-charged walls mediated by counterions is
studied using local molecular field (LMF) theory. Monte Carlo simulations of
the "mimic system'' given by LMF theory, with short-ranged "Coulomb core"
interactions in an effective single particle potential incorporating a
mean-field average of the long-ranged Coulomb interactions, provide a direct
test of the theory, and are in excellent agreement with more complex
simulations of the full Coulomb system by Moreira and Netz [Eur. Phys. J. E 8,
33 (2002)]. A simple, generally-applicable criterion to determine the
consistency parameter sigma_{min} needed for accurate use of the LMF theory is
presented
Organized condensation of worm-like chains
We present results relevant to the equilibrium organization of DNA strands of
arbitrary length interacting with a spherical organizing center, suggestive of
DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in
which a wrapping state is transformed into a complex multi-leafed, rosette
structure as the adhesion energy is reduced. The statistical mechanics of the
"melting" of a rosette can be mapped into an exactly soluble one-dimensional
many-body problem.Comment: 15 pages, 2 figures in a pdf fil
Why is the condensed phase of DNA preferred at higher temperature? DNA compaction in the presence of a multivalent cation
Upon the addition of multivalent cations, a giant DNA chain exhibits a large
discrete transition from an elongated coil into a folded compact state. We
performed single-chain observation of long DNAs in the presence of a
tetravalent cation (spermine), at various temperatures and monovalent salt
concentrations. We confirmed that the compact state is preferred at higher
temperatures and at lower monovalent salt concentrations. This result is
interpreted in terms of an increase in the net translational entropy of small
ions due to ionic exchange between higher and lower valence ions.Comment: 4pages,3figure
Structural Polymorphism of the Cytoskeleton: A Model of Linker-Assisted Filament Aggregation
The phase behavior of charged rods in the presence of inter-rod linkers is
studied theoretically as a model for the equilibrium behavior underlying the
organization of actin filaments by linker proteins in the cytoskeleton. The
presence of linkers in the solution modifies the effective inter-rod
interaction and can lead to inter-filament attraction. Depending on the
system's composition and physical properties such as linker binding energies,
filaments will either orient perpendicular or parallel to each other, leading
to network-like or bundled structures. We show that such a system can have one
of three generic phase diagrams, one dominated by bundles, another by networks,
and the third containing both bundle and network-like phases. The first two
diagrams can be found over a wide range of interaction energies, while the
third occurs only for a narrow range. These results provide theoretical
understanding of the classification of linker proteins as bundling proteins or
crosslinking proteins. In addition, they suggest possible mechanisms by which
the cell may control cytoskeletal morphology.Comment: 17 pages, 3 figure
Entropy-induced Microphase Separation in Hard Diblock Copolymers
Whereas entropy can induce phase behavior that is as rich as seen in
energetic systems, microphase separation remains a very rare phenomenon in
entropic systems. In this paper, we present a density functional approach to
study the possibility of entropy-driven microphase separation in diblock
copolymers. Our model system consists of copolymers composed of freely-jointed
slender hard rods. The two types of monomeric segments have comparable lengths,
but a significantly different diameter, the latter difference providing the
driving force for the phase separation. At the same time these systems can also
exhibit liquid crystalline phases. We treat this system in the appropriate
generalization of the Onsager approximation to chain-like particles. Using a
linear stability (bifurcation) analysis, we analytically determine the onset of
the microseparated and the nematic phases for long chains. We find that for
very long chains the microseparated phase always preempts the nematic. In the
limit of infinitely long chains, the correlations within the chain become
Gaussian and the approach becomes exact. This allows us to define a Gaussian
limit in which the theory strongly simplifies and the competition between
microphase separation and liquid crystal formation can be studied essentially
analytically. Our main results are phase diagrams as a function of the
effective diameter difference, the segment composition and the length ratio of
the segments. We also determine the amplitude of the positional order as a
function of position along the chain at the onset of the microphase separation
instability. Finally, we give suggestions as to how this type of
entropy-induced microphase separation could be observed experimentally.Comment: 16 pages, 7 figure
What do emulsification failure and Bose-Einstein condensation have in common?
Ideal bosons and classical ring polymers formed via self-assembly, are known
to have the same partition function, and so analogous phase transitions. In
ring polymers, the analogue of Bose-Einstein condensation occurs when a ring
polymer of macroscopic size appears. We show that a transition of the same
general form occurs within a whole class of systems with self-assembly, and
illustrate it with the emulsification failure of a microemulsion phase of
water, oil and surfactant. As with Bose-Einstein condensation, the transition
occurs even in the absence of interactions.Comment: 7 pages, 1 figure, typeset with EUROTeX, uses epsfi
Torsional fluctuations in columnar DNA assemblies
In columnar assemblies of helical bio-molecules the azimuthal degrees of
freedom, i.e. rotations about the long axes of molecules, may be important in
determining the structure of the assemblies especially when the interaction
energy between neighbouring molecules explicitly depends on their relative
azimuthal orientations. For DNA this leads to a rich variety of mesophases for
columnar assemblies, each categorized by a specific azimuthal ordering. In a
preceding paper [A. Wynveen, D. J. Lee, and A. A. Kornyshev, Eur. Phys. J. E,
16, 303 (2005)] a statistical mechanical theory was developed for the
assemblies of torsionally rigid molecues in order to determine how thermal
fluctuations influence the structure of these mesophases. Here we extend this
theory by including torsional fluctuations of the molecules, where a DNA
molecule may twist about its long axis at the cost of torsional elastic energy.
Comparing this with the previous study, we find that inclusion of torsional
fluctuations further increases the density at which the transition between the
hexagonal structure and the predicted rhombic phase occurs and reduces the
level of distortion in the rhombic phase. As X-ray diffraction may probe the
2-D lattice structure of such assemblies and provide information concerning the
underlying interaction between molecules, we have also calculated correlation
functions for the azimuthal ordering which are manifest in an x-ray scattering
intensity profiles.Comment: 33 pages, 8 figure
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