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

Osmotic force resisting chain insertion in a colloidal suspension

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accomodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fraction for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm.Comment: 16 pages,3 figures. Accepted for publication in European Physical Journal

Measuring the force ejecting DNA from phage

We discuss how a balance can be established between the force acting to eject DNA from viral capsids and the force resisting its entry into a colloidal suspension which mimics the host cell cytoplasm. The ejection force arises from the energy stored in the capsid as a consequence of the viral genome (double-stranded DNA) being strongly bent and crowded on itself. The resisting force is associated with the osmotic pressure exerted by the colloidal particles in the host solution. Indeed, recent experimental work has demonstrated that the extent of ejection can be progressively limited by increasing the external osmotic pressure; at a sufficiently high pressure the ejection is completely suppressed. We outline here a theoritical analysis that allows a determination of the internal (capsid) pressure by examining the different relations between force and pressure inside and outside the capsid, using the experimentally measured position of the force balance.Comment: 15 pages, 4 figures, accepted for publication in J. Phys. Chem

Dichotomy for generic supercuspidal representations of G2G_2

The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of $G_2$ over a $p$-adic field, one can associate a generic supercuspidal irreducible representation of either $PGSp_6$ or$PGL_3$. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of $G_2$ and other representations of $PGSp_6$ and $PGL_3$. This correspondence arises from theta correspondences in $E_6$ and $E_7$, analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irreducible representations of $G_2$ to a single conjecture about the parameterization for $PGSp_6$.Comment: Version 2: Mistakes in Prop 3.2 and 3.5 corrected. Results strengthened in case p=2. Changes made throughout for consistency with stronger results and reformulatio

Spontaneous patterning of quantum dots at the air-water interface

Nanoparticles deposited at the air-water interface are observed to form circular domains at low density and stripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competition between an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential with attractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have a potential use in nanoelectronic applications

Orbital L-functions for the space of binary cubic forms

We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from the intrinsic interest, results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper (arXiv:1102.2914).Comment: 49 pages; submitte

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of all sphere-like viruses adopt icosahedral symmetry. In the present paper we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal "switching" configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins.Comment: pdf file, 13 pages, three 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