We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. We include an alternative derivation of this result directly from Haiman’s work on Schur positive immanants. Our results imply an intriguing log-concavity propert...

Chi-Kwong Li,1 Mikio Nakahara,2 Yiu-Tung Poon,3 Nung-Sing Sze,4 and Hiroyuki Tomita5 Department of Mathematics, College of William & Mary, Williamsburg, VA 23187-8795, USA.∗ Research Center for Quantum Computing and Department of Physics, Kinki University, 3-4-1 Kowakae, Higashi-Osaka, 577-8502, Japan.† Department of Mathematics, Iowa State University, Ames, IA 50051, USA.‡ Department of Applie...

Let A denote the alternation limit algebra, studied by Hopenwasser and Power, and by Poon, which is the closed direct limit of upper triangular matrix algebras determined by refinement embeddings of multiplicity rk and standard embeddings of multiplicity sk. It is shown that the quotient of the isometric automorphism group by the approximately inner automorphisms is the abelian group ZZ where d...

This article offers a modification of Chow and Liu's learning algorithm in the context of handwritten digit recognition. The modi­ fied algorithm directs the user to group digits into several classes consisting of digits that are hard to distinguish and then construct­ ing an optimal conditional tree representa­ tion for each class of digits instead of for each single digit as done by Chow and ...

Centenarians are survivors, and many among them exemplify sustained competence into very old age. This paper highlights three important resilience domains among centenarians: personal resilience (e.g., personality), cognitive resilience (e.g., intellectual functioning), and social and economic resilience (e.g., social support and economic resources). Disciplines Gerontology Comments This chapte...

John S. Ho, Yuji Tanabe, Shrivats Mohan Iyer, Amelia J. Christensen, Logan Grosenick, 3 Karl Deisseroth, 3, 4, 5, 6 Scott L. Delp, 7 and Ada S. Y. Poon Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA Department of Bioengineering, Stanford University, Stanford, California 94305, USA Neurosciences Program, Stanford University, Stanford, California 94305,...

We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by σ x , σ ⊗n y and σ ⊗n z , where n > 2 is the number of qubits encoding the codeword. It is proved that Email addresses: [email protected] (Chi-Kwong Li), [email protected] (Mikio Nakahara), yt...

This paper presents a GARCH type volatility model with a time-varying unconditional volatility which is a function of macroeconomic information. It is an extension of the SPLINE GARCH model proposed by Engle and Rangel (2005). The advantage of the model proposed in this paper is that the macroeconomic information available (and/or forecasts) is used in the parameter estimation process. Based on...

In this paper we present a polynomial-time procedure to find a low rank solution for a system of Linear Matrix Inequalities (LMI). The existence of such a low rank solution was shown in AuYeung and Poon [1] and Barvinok [3]. In Au-Yeung and Poon’s approach, an earlier unpublished manuscript of Bohnenblust [6] played an essential role. Both proofs in [1] and [3] are nonconstructive in nature. Th...

We give a counterexample to a conjecture of Poon [Poo06] that any orthogonal tree in two dimensions can always be flattened by a continuous motion that preserves edge lengths and avoids self-intersection. We show our example is locked by extending results on strongly locked self-touching linkages due to Connelly, Demaine and Rote [CDR02] to allow zero-length edges as defined in [ADG07], which m...