An extension of Tamari lattices

For any finite path $v$ on the square grid consisting of north and east unit steps, starting at (0,0), we construct a poset Tam$(v)$ that consists of all the paths weakly above $v$ with the same number of north and east steps as $v$. For particular choices of $v$, we recover the traditional Tamari lattice and the $m$-Tamari lattice. Let $\overleftarrow{v}$ be the path obtained from $v$ by reading the unit steps of $v$ in reverse order, replacing the east steps by north steps and vice versa. We show that the poset Tam$(v)$ is isomorphic to the dual of the poset Tam$(\overleftarrow{v})$. We do so by showing bijectively that the poset Tam$(v)$ is isomorphic to the poset based on rotation of full binary trees with the fixed canopy $v$, from which the duality follows easily. This also shows that Tam$(v)$ is a lattice for any path $v$. We also obtain as a corollary of this bijection that the usual Tamari lattice, based on Dyck paths of height $n$, is a partition of the (smaller) lattices Tam$(v)$, where the $v$ are all the paths on the square grid that consist of $n-1$ unit steps. We explain possible connections between the poset Tam$(v)$ and (the combinatorics of) the generalized diagonal coinvariant spaces of the symmetric group.Comment: 18 page

From generalized Tamari intervals to non-separable planar maps

International audienceLet v be a grid path made of north and east steps. The lattice TAM(v), based on all grid paths weakly above the grid path v sharing the same endpoints as v, was introduced by Pre ́ville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case v = (NE)n. They showed that TAM(v) is isomorphic to the dual of TAM(←−v ), where ←−v is the reverse of v with N and E exchanged. Our main contribution is a bijection from intervals in TAM(v) to non-separable planar maps. It follows that the number of intervals in TAM(v) over all v of length n is 2(3n+3)! (n+2)!(2n+3)! . This formula was first obtained by Tutte(1963) for non-separable planar maps

Matal v. Tam Revisited

The Supreme Court’s ruling this past summer in Matal v. Tam was more than just a decision on the titles that could be used when registering one’s mark, it was also a vindication to those whom slurs have been used against; an opportunity to reclaim the word and change its meaning or at the very least, attach new feelings to it. This was the noble goal underlying lead singer, Simon Tam, of the rock group, “The Slants” action about a decade ago. Tam recalls that growing up “the notion of having slanted eyes was always considered a negative thing…and kids would pull their eyes back in a slant-eyed gesture to make fun of us and I wanted to change it to something that was powerful, something that was considered beautiful.” This post was originally published on the Cardozo Arts & Entertainment Law Journal website on January 17, 2018. The original post can be accessed via the Archived Link button above

USA v. Kin Tam

USDC for the Eastern District of Pennsylvani

Salient Object Detection via Augmented Hypotheses

In this paper, we propose using \textit{augmented hypotheses} which consider objectness, foreground and compactness for salient object detection. Our algorithm consists of four basic steps. First, our method generates the objectness map via objectness hypotheses. Based on the objectness map, we estimate the foreground margin and compute the corresponding foreground map which prefers the foreground objects. From the objectness map and the foreground map, the compactness map is formed to favor the compact objects. We then derive a saliency measure that produces a pixel-accurate saliency map which uniformly covers the objects of interest and consistently separates fore- and background. We finally evaluate the proposed framework on two challenging datasets, MSRA-1000 and iCoSeg. Our extensive experimental results show that our method outperforms state-of-the-art approaches.Comment: IJCAI 2015 pape

Tam Nguyen v. Commonwealth of Pennsylvania

USDC for the Eastern District of Pennsylvani

Modeling of power electronic systems with EMTP

In view of the potential impact of power electronics on power systems, there is need for a computer modeling/analysis tool to perform simulation studies on power systems with power electronic components as well as to educate engineering students about such systems. The modeling of the major power electronic components of the NASA Space Station Freedom Electric Power System is described along with ElectroMagnetic Transients Program (EMTP) and it is demonstrated that EMTP can serve as a very useful tool for teaching, design, analysis, and research in the area of power systems with power electronic components. EMTP modeling of power electronic circuits is described and simulation results are presented