291 citations · 336 across the 16 of their papers we have counts for
7 papers · 1 filter
On the Spectrum of Middle-Cubes
Ke Qiu, Rong Qiu, Yong Jiang +1
A middle-cube is an induced subgraph consisting of nodes at the middle two layers of a hypercube. The middle-cubes are related to the well-known Revolving Door (Middle Levels) conj…
A bound on the scrambling index of a primitive matrix using Boolean rank
Mahmud Akelbek, Sandra Fital, Jian Shen
The scrambling index of an primitive matrix is the smallest positive integer such that , where denotes the transpose of and denote…
On the Borel-Cantelli Lemma and its Generalization
Chunrong Feng, Liangpan Li, Jian Shen
Let be a sequence of events on a probability space . We show that if …
On the Chudnovsky-Seymour-Sullivan Conjecture on Cycles in Triangle-free Digraphs
Kevin Chen, Sean Karson, Dan Liu +1
For a simple digraph without directed triangles or digons, let be the size of the smallest subset such that has no directed cycles, and…
Analyzing the Accuracy of the Fitch Method for Reconstructing Ancestral States on Ultrametric Phylogenies
Louxin Zhang, Jian Shen, Jialiang Yang +1
Recurrence formulas are presented for studying the accuracy of the Fitch method for reconstructing the ancestral states in a given phylogenetic tree. As their applications, we anal…
A sum-division estimate of reals
Liangpan Li, Jian Shen
Let be a finite set of positive real numbers. We present a sum-division estimate: |A+A|^2|A/A|\geq\frac{|A|^4}{4}.
Thermodynamics of Information Retrieval
Kostadin Koroutchev, Jian Shen, Elka Koroutcheva +1
In this work, we suggest a parameterized statistical model (the gamma distribution) for the frequency of word occurrences in long strings of English text and use this model to buil…