Computing the Ball Size of Frequency Permutations under Chebyshev Distance

Let $S_n^\lambda$ be the set of all permutations over the multiset $\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where $n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of $S_n^\lambda$ in which every two elements have distance at least $d$. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii. We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Both methods extend previous known results. The first one runs in $O({2d\lambda \choose d\lambda}^{2.376}\log n)$ time and $O({2d\lambda \choose d\lambda}^{2})$ space. The second one runs in $O({2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}\frac{n}{\lambda})$ time and $O({2d\lambda \choose d\lambda})$ space. For small constants $\lambda$ and $d$, both are efficient in time and use constant storage space.Comment: Submitted to ISIT 201

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Multimodal News Summarization, Tracking and Annotation Incorporating Tensor Analysis of Memes

We demonstrate four novel multimodal methods for efficient video summarization and comprehensive cross-cultural news video understanding. First, For video quick browsing, we demonstrate a multimedia event recounting system. Based on nine people-oriented design principles, it summarizes YouTube-like videos into short visual segments (812sec) and textual words (less than 10 terms). In the 2013 Trecvid Multimedia Event Recounting competition, this system placed first in recognition time efficiency, while remaining above average in description accuracy. Secondly, we demonstrate the summarization of large amounts of online international news videos. In order to understand an international event such as Ebola virus, AirAsia Flight 8501 and Zika virus comprehensively, we present a novel and efficient constrained tensor factorization algorithm that first represents a video archive of multimedia news stories concerning a news event as a sparse tensor of order 4. The dimensions correspond to extracted visual memes, verbal tags, time periods, and cultures. The iterative algorithm approximately but accurately extracts coherent quad-clusters, each of which represents a significant summary of an important independent aspect of the news event. We give examples of quad-clusters extracted from tensors with at least 108 entries derived from international news coverage. We show the method is fast, can be tuned to give preferences to any subset of its four dimensions, and exceeds three existing methods in performance. Thirdly, noting that the co-occurrence of visual memes and tags in our summarization result is sparse, we show how to model cross-cultural visual meme influence based on normalized PageRank, which more accurately captures the rates at which visual memes are reposted in a specified time period in a specified culture. Lastly, we establish the correspondences of videos and text descriptions in different cultures by reliable visual cues, detect culture-specific tags for visual memes and then annotate videos in a cultural settings. Starting with any video with less text or no text in one culture (say, US), we select candidate annotations in the text of another culture (say, China) to annotate US video. Through analyzing the similarity of images annotated by those candidates, we can derive a set of proper tags from the viewpoints of another culture (China). We illustrate cultural-based annotation examples by segments of international news. We evaluate the generated tags by cross-cultural tag frequency, tag precision, and user studies

Influence of migration policy risk on international market segmentation: analysis of housing and rental markets in the euro area

This paper aims to discuss the influence of migration policy risk on market segmentation of housing and rental markets in the Euro Area. Policy risk is represented by the Migration Policy Uncertainty Index (MPUI) and Migration Fear Index (MFI) of Germany and the United Kingdom; in this study, whether these indexes influence the interaction between the housing and rental markets of the two countries and euro-area countries was examined. The empirical results showed that the influence of the United Kingdom’s migration policy risk on the euro-area countries is higher than that of Germany. The United Kingdom’s MPUI and MFI significantly contribute to the influence of the United Kingdom’s housing market on other markets except for Belgium and Spain. Compared with housing market connectedness, the rental market connectedness is less influenced by migration policy risk and migration fear. This may be because variables related to short-term residence policies influence the rental market. The high policy risk is more likely to influence decisions related to long-term house purchase, but not those related to short-term residence. Finally, this study found that the higher the uncertainty of the migration policies of the United Kingdom and Germany is, the higher the house market segmentation is

Biodegradation of phenol and 2-chlorophenol using a fill-and-draw-reactor

The biological degradation of phenol and 2-chlorophenol was studied at room temperature in a microprocesser controlled fill-and-draw reactor using activated sludge from the Passaic Valley Sewerage Commissioners wastewater treatment plant (Newark, New Jersey). The reactor was cycled through four unit processes: fill, react, settle, and draw. Different cycle times were tested, and the system response was characterized by dissolved oxygen measurements and substrate analysis (by gas chromatography). With inhibitory substrates, such as those tested, this reactor had much more flexibility, and was therefore much easier to operate, than a standard continuous flow reactor