1,939 research outputs found
Dichotomy for generic supercuspidal representations of
The local Langlands conjectures imply that to every generic supercuspidal
irreducible representation of over a -adic field, one can associate a
generic supercuspidal irreducible representation of either or.
We prove this conjectural dichotomy, demonstrating a precise correspondence
between certain representations of and other representations of
and . This correspondence arises from theta correspondences in and
, analysis of Shalika functionals, and spin L-functions. Our main result
reduces the conjectural Langlands parameterization of generic supercuspidal
irreducible representations of to a single conjecture about the
parameterization for .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
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
Samuel Usque: A Consolation for the Tribulations of Israel, Third Dialogue
The closing decade of the fifteenth century, which opened up new continents and new horizons for humanity in general, produced in the narrower circle of the Jewish world a series of cataclysmic upheavals which convulsed the entire body of Israel with the agony of imminent extinction. This trumpet call of fate, though crushing the body, aroused the spirit from the lethargy of wretched smugness, veering it violently from the rut of a present, that led nowhere, into the unfamiliar road linking the past with the future. There arose the desire to examine into the forgotten nooks of the past while the eye seeking the future lost itself in the mystic vapors of a yet unborn sunrise. Thus historical interest and national mysticism came to the forefront of the Jewish consciousness
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
Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms
Let be an unramified prime in a totally real field such that
. Our main result shows that Hilbert modular newforms of parallel
weight two for can be constructed naturally, via classical theta
series, from modules of isogenies of superspecial abelian varieties with real
multiplication on a Hilbert moduli space. This can be viewed as a geometric
reinterpretation of the Eichler Basis Problem for Hilbert modular forms.Comment: to appear in J.N.
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
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