A Modified KZ Reduction Algorithm

The Korkine-Zolotareff (KZ) reduction has been used in communications and cryptography. In this paper, we modify a very recent KZ reduction algorithm proposed by Zhang et al., resulting in a new algorithm, which can be much faster and more numerically reliable, especially when the basis matrix is ill conditioned.Comment: has been accepted by IEEE ISIT 201

A Linearithmic Time Algorithm for a Shortest Vector Problem in Compute-and-Forward Design

We propose an algorithm with expected complexity of \bigO(n\log n) arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm is more efficient than the best known algorithms with proved complexity.Comment: It has been submitted to ISIT 201

Nucleon partonic spin structure to be explored by the unpolarized Drell-Yan program of COMPASS experiment at CERN

The observation of the violation of Lam-Tung relation in the $\pi N$ Drell-Yan process triggered many theoretical speculations. The TMD Boer-Mulders functions characterizing the correlation of transverse momentum and transverse spin for partons in unpolarized hadrons could nicely account for the violation. The COMPASS experiment at CERN will measure the angular distributions of dimuons from the unpolarized Drell-Yan process over a wide kinematic region and study the beam particle dependence. Significant statistics is expected from a successful run in 2015 which will bring further understanding of the origin of the violation of Lam-Tung relation and of the partonic transverse spin structure of the nucleon.Comment: Proceedings of the 21st International Symposium on Spin Physics - October 20-24, 2014, Beijing, China; 6 pages, 3 figures, 1 tabl

Selective gating of neuronal activity by intrinsic properties in distinct motor rhythms

This research has been supported by the Royal Society, Wellcome Trust (089319), and the Biotechnology and Biological Sciences Research Council (BB/L0011X/1). I thank Drs. Steve Soffe, Alan Roberts, Erik Svensson, Hong-Yan Zhang, and Stefan Pulver for commenting on the manuscript.Many neural circuits show fast reconfiguration following altered sensory or modulatory inputs to generate stereotyped outputs. In the motor circuit of Xenopus tadpoles, I study how certain voltage-dependent ionic currents affect firing thresholds and contribute to circuit reconfiguration to generate two distinct motor patterns, swimming and struggling. Firing thresholds of excitatory interneurons [i.e., descending interneurons (dINs)] in the swimming central pattern generator are raised by depolarization due to the inactivation of Na+ currents. In contrast, the thresholds of other types of neurons active in swimming or struggling are raised by hyperpolarization from the activation of fast transient K+ currents. The firing thresholds are then compared with the excitatory synaptic drives, which are revealed by blocking action potentials intracellularly using QX314 during swimming and struggling. During swimming, transient K+ currents lower neuronal excitability and gate out neurons with weak excitation, whereas their inactivation by strong excitation in other neurons increases excitability and enables fast synaptic potentials to drive reliable firing. During struggling, continuous sensory inputs lead to high levels of network excitation. This allows the inactivation of Na+ currents and suppression of dIN activity while inactivating transient K+ currents, recruiting neurons that are not active in swimming. Therefore, differential expression of these currents between neuron types can explain why synaptic strength does not predict firing reliability/intensity during swimming and struggling. These data show that intrinsic properties can override fast synaptic potentials, mediate circuit reconfiguration, and contribute to motor–pattern switching.Publisher PDFPeer reviewe

On the Success Probability of the Box-Constrained Rounding and Babai Detectors

In communications, one frequently needs to detect a parameter vector \hbx in a box from a linear model. The box-constrained rounding detector \x^\sBR and Babai detector \x^\sBB are often used to detect \hbx due to their high probability of correct detection, which is referred to as success probability, and their high efficiency of implimentation. It is generally believed that the success probability P^\sBR of \x^\sBR is not larger than the success probability P^\sBB of \x^\sBB. In this paper, we first present formulas for P^\sBR and P^\sBB for two different situations: \hbx is deterministic and \hbx is uniformly distributed over the constraint box. Then, we give a simple example to show that P^\sBR may be strictly larger than P^\sBB if \hbx is deterministic, while we rigorously show that P^\sBR\leq P^\sBB always holds if \hbx is uniformly distributed over the constraint box.Comment: to appear in ISIT 201

Frobenius morphisms and stability conditions

We generalize Deng-Du's folding argument, for the bounded derived category $\mathcal{D}(Q)$ of an acyclic quiver $Q$, to the finite dimensional derived category $\mathcal{D}(\Gamma Q)$ of the Ginzburg algebra $\Gamma Q$ associated to $Q$. We show that the $F$-stable category of $\mathcal{D}(\Gamma Q)$ is equivalent to the finite dimensional derived category $\mathcal{D}(\Gamma\mathbb{S})$ of the Ginzburg algebra $\Gamma\mathbb{S}$ associated to the species $\mathbb{S}$, which is folded from $Q$. If $(Q,\mathbb{S})$ is of Dynkin type, we prove that $\operatorname{Stab}\mathcal{D}(\mathbb{S})$ (resp. the principal component $\operatorname{Stab}^\circ\mathcal{D}(\Gamma\mathbb{S})$) of the space of the stability conditions of $\mathcal{D}(\mathbb{S})$ (resp. $\mathcal{D}(\Gamma\mathbb{S})$) is canonically isomorphic to $\operatorname{FStab}\mathcal{D}(Q)$ (resp. the principal component $\operatorname{FStab}^\circ\mathcal{D}(\Gamma Q)$) of the space of $F$-stable stability conditions of $\mathcal{D}(Q)$ (resp. $\mathcal{D}(\Gamma Q)$). There are two applications. One is for the space $\operatorname{NStab}\mathcal{D}(\Gamma Q)$ of numerical stability conditions in $\operatorname{Stab}^\circ\mathcal{D}(\Gamma Q)$. We show that $\operatorname{NStab}\mathcal{D}(\Gamma Q)$ consists of $\operatorname{Br} Q/\operatorname{Br} \mathbb{S}$ many connected components, each of which is isomorphic to $\operatorname{Stab}^\circ\mathcal{D}(\Gamma\mathbb{S})$, for $(Q,\mathbb{S})$ is of type $(A_3, B_2)$ or $(D_4, G_2)$. The other is that we relate the $F$-stable stability conditions to the Gepner type stability conditions.Comment: Update versio