The Bergman kernel of the symmetrized polydisc in higher dimensions has zeros

We prove that the Bergman kernel of the symmetrized polydisc in dimension greater than two has zeros.Comment: ESI preprint 174

Are you a Good Employee or Simply a Good Guy? Infl?uence Costs and Contract Design.

We develop a principal-agent model with a moral hazard problem in which the principal has access to a hard signal (the level of output) and a soft signal (the supervision signal) about the agent?s level of effort. We show that the agent?'s ability to manipulate the soft signal increases the cost of implementing the effcient equilibrium, leading to wage compression when the infl?uence cost is privately incurred by the agent. When manipulation activities negatively affect the agent?s productivity through the level of output, the design of infl?uence-free contracts that deter manipulation may lead to high-powered incentives. This result implies that high-productivity workers face incentive schemes that are more sensitive to hard evidence than those faced by their low-productivity counterparts. In that context, the principal will tolerate infl?uence for low-productivity workers but not for high-productivity workers. We also fi?nd that in the case of productivity-based costs, it may be optimal for the principal not to supervise the agent, even if supervision is costless.principal-agent model with supervision, contract design, in?uence activities, manipulation, productivity-based influence costs, power of incentives

Electromagnetic Source Imaging via a Data-Synthesis-Based Convolutional Encoder-Decoder Network

Electromagnetic source imaging (ESI) requires solving a highly ill-posed inverse problem. To seek a unique solution, traditional ESI methods impose various forms of priors that may not accurately reflect the actual source properties, which may hinder their broad applications. To overcome this limitation, in this paper a novel data-synthesized spatio-temporally convolutional encoder-decoder network method termed DST-CedNet is proposed for ESI. DST-CedNet recasts ESI as a machine learning problem, where discriminative learning and latent-space representations are integrated in a convolutional encoder-decoder network (CedNet) to learn a robust mapping from the measured electroencephalography/magnetoencephalography (E/MEG) signals to the brain activity. In particular, by incorporating prior knowledge regarding dynamical brain activities, a novel data synthesis strategy is devised to generate large-scale samples for effectively training CedNet. This stands in contrast to traditional ESI methods where the prior information is often enforced via constraints primarily aimed for mathematical convenience. Extensive numerical experiments as well as analysis of a real MEG and Epilepsy EEG dataset demonstrate that DST-CedNet outperforms several state-of-the-art ESI methods in robustly estimating source signals under a variety of source configurations.Comment: 15 pages, 14 figures, and journa

On the spectrum of Dehn twists in quantum Teichmuller theory

The operator realizing a Dehn twist in quantum Teichmuller theory is diagonalized and continuous spectrum is obtained. This result is in agreement with the expected spectrum of conformal weights in quantum Liouville theory at c>1. The completeness condition of the eigenvectors includes the integration measure which appeared in the representation theoretic approach to quantum Liouville theory by Ponsot and Teschner. The underlying quantum group structure is also revealed.Comment: 13 pages,8 figures,LaTeX2

Towards an operator-algebraic construction of integrable global gauge theories

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species transforming under a global gauge group. Starting from a two-particle S-matrix satisfying the usual requirements (unitarity, Yang-Baxter equation, Poincar\'e and gauge invariance, crossing symmetry, ...), a pair of relatively wedge-local quantum fields is constructed which determines the field net of the model. Although the verification of the modular nuclearity condition as a criterion for the existence of local fields is not carried out in this paper, arguments are presented that suggest it holds in typical examples such as nonlinear O(N) sigma-models. It is also shown that for all models complying with this condition, the presented construction solves the inverse scattering problem by recovering the S-matrix from the model via Haag-Ruelle scattering theory, and a proof of asymptotic completeness is given.Comment: 27 pages. Corrected a few minor typos and added a paragraph in the conclusions to comply with published versio

A1(1)A_1^{(1)} Admissible Representations -- Fusion Transformations and Local Correlators

We reconsider the earlier found solutions of the Knizhnik-Zamolodchikov (KZ) equations describing correlators based on the admissible representations of $A_1^{(1)}$. Exploiting a symmetry of the KZ equations we show that the original infinite sums representing the 4-point chiral correlators can be effectively summed up. Using these simplified expressions with proper choices of the contours we determine the duality (braid and fusion) transformations and show that they are consistent with the fusion rules of Awata and Yamada. The requirement of locality leads to a 1-parameter family of monodromy (braid) invariants. These analogs of the ``diagonal'' 2-dimensional local 4-point functions in the minimal Virasoro theory contain in general non-diagonal terms. They correspond to pairs of fields of identical monodromy, having one and the same counterpart in the limit to the Virasoro minimal correlators.Comment: LaTex, 20 pages; misprints corrected, few small addition

Proteomic Analysis of a Noninvasive Human Model of Acute Inflammation and Its Resolution: The Twenty-one Day Gingivitis Model

The 21-day experimental gingivitis model, an established noninvasive model of inflammation in response to increasing bacterial accumulation in humans, is designed to enable the study of both the induction and resolution of inflammation. Here, we have analyzed gingival crevicular fluid, an oral fluid comprising a serum transudate and tissue exudates, by LC−MS/MS using Fourier transform ion cyclotron resonance mass spectrometry and iTRAQ isobaric mass tags, to establish meta-proteomic profiles of inflammation-induced changes in proteins in healthy young volunteers. Across the course of experimentally induced gingivitis, we identified 16 bacterial and 186 human proteins. Although abundances of the bacterial proteins identified did not vary temporally, Fusobacterium outer membrane proteins were detected. Fusobacterium species have previously been associated with periodontal health or disease. The human proteins identified spanned a wide range of compartments (both extracellular and intracellular) and functions, including serum proteins, proteins displaying antibacterial properties, and proteins with functions associated with cellular transcription, DNA binding, the cytoskeleton, cell adhesion, and cilia. PolySNAP3 clustering software was used in a multilayered analytical approach. Clusters of proteins that associated with changes to the clinical parameters included neuronal and synapse associated proteins