Geometrical Realization of Beutler-Fano formulas appearing in eigenphase shifts and time delays in multichannel scattering

Recently, we showed that eigenphase shifts and eigentime delays near a resonance for a system of one discrete state and two continua are functionals of the Beutler-Fano formula using appropriate dimensionless energy units and line profile indices and identified parameters responsible for the avoided crossing of eigenphase shifts and eigentime delays and also identified parameters responsible for the eigentime delays due to a change in frame transformation. In this paper, the geometrical realization of the Beutler-Fano formulas is considered in the three-dimensional Liouville space spanned by the Pauli matrices, where dynamic operators are vectors. Vectors corresponding to the background scattering matrix, the S matrix, and the time delay matrix Q form a spherical triangle whose vertex and edge angles are parameters pertaining to the frame transformations among eigenchannels of those matrices and eigenphase shifts of the scattering matrices and the phase shift due to a resonance scattering. The cotangent laws of the spherical triangle yield Beutler-Fano resonance formulas appearing in eigenphase shifts and time delays. Duality holding for the spherical triangle explains the symmetry observed in the relations among parameters and provides a systematic way of defining conjugate dynamic parameters. The spherical triangle also shows the rule of combining the channel-channel couplings in the background scattering with the resonant interaction to give the avoided crossing interactions in the curves of eigenphase shifts as functions of eneryg. The theory developed in the previous and present papers is applied to the vibrational predissociation of triatomic van der Waals molecules.Comment: 26 pages, 7 figures, RevTeX, will be submitted to Phys. Rev. A, Major conceptual change

On the uniqueness of Ricci flow

In this note, we study the problem of uniqueness of Ricci flow on complete noncompact manifolds. We consider the class of solutions with curvature bounded above by C/t when t > 0. In paricular, we proved uniqueness if in addition the initial curvature is of polynomial growth and Ricci curvature of the flow is relatively small.Comment: All comments are welcome

Hermitian manifolds with quasi-negative curvature

In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of Chern-Ricci curvature will be preserved if the initial metric has non-positive bisectional curvature. As an application, we show that the canonical line bundle of a compact Hermitian manifold with nonpositive bisectional curvature and quasi-negative Chern-Ricci curvature is ample.Comment: final version to appear in Math. Ann. arXiv admin note: text overlap with arXiv:1812.0461

Signal Space Alignment for an Encryption Message and Successive Network Code Decoding on the MIMO K-way Relay Channel

This paper investigates a network information flow problem for a multiple-input multiple-output (MIMO) Gaussian wireless network with $K$-users and a single intermediate relay having $M$ antennas. In this network, each user intends to convey a multicast message to all other users while receiving $K-1$ independent messages from the other users via an intermediate relay. This network information flow is termed a MIMO Gaussian $K$-way relay channel. For this channel, we show that $\frac{K}{2}$ degrees of freedom is achievable if $M=K-1$. To demonstrate this, we come up with an encoding and decoding strategy inspired from cryptography theory. The proposed encoding and decoding strategy involves a \textit{signal space alignment for an encryption message} for the multiple access phase (MAC) and \textit{zero forcing with successive network code decoding} for the broadcast (BC) phase. The idea of the \emph{signal space alignment for an encryption message} is that all users cooperatively choose the precoding vectors to transmit the message so that the relay can receive a proper encryption message with a special structure, \textit{network code chain structure}. During the BC phase, \emph{zero forcing combined with successive network code decoding} enables all users to decipher the encryption message from the relay despite the fact that they all have different self-information which they use as a key.Comment: 5 pages, 3 figures, and submitted ICC 201

Negative Example Aided Transcription Factor Binding Site Search

Computational approaches to transcription factor binding site identification have been actively researched for the past decade. Negative examples have long been utilized in de novo motif discovery and have been shown useful in transcription factor binding site search as well. However, understanding of the roles of negative examples in binding site search is still very limited. We propose the 2-centroid and optimal discriminating vector methods, taking into account negative examples. Cross-validation results on E. coli transcription factors show that the proposed methods benefit from negative examples, outperforming the centroid and position-specific scoring matrix methods. We further show that our proposed methods perform better than a state-of-the-art method. We characterize the proposed methods in the context of the other compared methods and show that, coupled with motif subtype identification, the proposed methods can be effectively applied to a wide range of transcription factors. Finally, we argue that the proposed methods are well-suited for eukaryotic transcription factors as well. Software tools are available at: http://biogrid.engr.uconn.edu/tfbs_search/.Comment: 14 pages, 16 figure

The K\"ahler Ricci flow around complete bounded curvature K\"ahler metrics

We produce complete bounded curvature solutions to K\"ahler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth \K metric uniformly equivalent to another complete bounded curvature \K metric. We obtain related flow results for non-smooth as well as degenerate initial conditions. We also obtain a stability result for complex space forms under the flow.Comment: 22 pages; editions made to earlier version (including revision of title, addition to Theorem 1.2 and correction in proof of Claim 2.2

Complex manifolds with negative curvature operator

We prove that compact complex manifolds with admitting metrics with negative Chern curvature operator either admit a $dd^c$-exact positive (1,1) current, or are K\"ahler with ample canonical bundle. In the case of complex surfaces we obtain a complete classification. The proofs rely on a global existence and convergence result for the pluriclosed flow

Individual Preference Aware Caching Policy Design in Wireless D2D Networks

Cache-aided wireless device-to-device (D2D) networks allow significant throughput increase, depending on the concentration of the popularity distribution of files. Many studies assume that all users have the same preference distribution; however, this may not be true in practice. This work investigates whether and how the information about individual preferences can benefit cache-aided D2D networks. We examine a clustered network and derive a network utility that considers both the user distribution and channel fading effects into the analysis. We also formulate a utility maximization problem for designing caching policies. This maximization problem can be applied to optimize several important quantities, including throughput, energy efficiency (EE), cost, and hit-rate, and to solve different tradeoff problems. We provide a general approach that can solve the proposed problem under the assumption that users coordinate, then prove that the proposed approach can obtain the stationary point under a mild assumption. Using simulations of practical setups, we show that performance can improve significantly with proper exploitation of individual preferences. We also show that different types of tradeoffs exist between different performance metrics and that they can be managed through caching policy and cooperation distance designs.Comment: Accepted by IEEE Transactions on Wireless Communication

Chern-Ricci flows on noncompact complex manifolds

In this work, we obtain existence criteria for Chern-Ricci flows on noncompact manifolds. We generalize a result by Tossati-Wienkove on Chern-Ricci flows to noncompact manifolds and at the same time generalize a result for Kahler-Ricci flows by Lott-Zhang to Chern-Ricci flows. Using the existence results, we prove that any complete noncollapsed Kahler metric with nonnegative bisectional curvature on a noncompact complex manifold can be deformed to a complete Kahler metric with nonnegative and bounded bisectional curvature which will have maximal volume growth if the initial metric has maximal volume. Combining this result with the result of Chau-Tam, we give another proof that a complete noncompact Kahler manifold with nonnegative bisectional curvature (not necessarily bounded) and maximal volume growth is biholomorphic to the complex Euclidean space. This last result has already been proved by Gang Liu recently using other methods. This last result is partial confirmation of a uniformization conjecture of Yau.Comment: some results added; printing mistakes correcte

Wrong-sign Kaons in B decays and New Physics

New physics can possibly emerge in the B decays into wrong-sign kaons for which the standard model contributions are extremely suppressed. We analyze two-body decays of $\bar{B}^0$ and $B^-$ mesons involving the $b\to dd\bar{s}$ ($\Delta S=-1$) and $b\to ss\bar{d}$ ($\Delta S=+2$) transitions in a model independent way, and examine various wrong-sign kaon signals which are expected to be observed in the future $B$ experiments. Our analysis shows that it would be possible to identify the origin of new physics through the combined analysis of several B decay modes involving one or two wrong-sign $K^*$'s.Comment: 16 pages, revtex