2,202 research outputs found
A Polynomial time Algorithm for Hamilton Cycle with maximum Degree 3
Based on the famous Rotation-Extension technique, by creating the new
concepts and methods: broad cycle, main segment, useful cut and insert,
destroying edges for a main segment, main goal Hamilton cycle, depth-first
search tree, we develop a polynomial time algorithm for a famous NPC: the
Hamilton cycle problem. Thus we proved that NP=P. The key points of this paper
are: 1) there are two ways to get a Hamilton cycle in exponential time: a full
permutation of n vertices; or, chose n edges from all k edges, and check all
possible combinations. The main problem is: how to avoid checking all
combinations of n edges from all edges. My algorithm can avoid this. Lemma 1
and lemma 2 are very important. They are the foundation that we always can get
a good branch in the depth-first search tree and can get a series of destroying
edges (all are bad edges) for this good branch in polynomial time. The
extraordinary insights are: destroying edges, a tree contains each main segment
at most one time at the same time, and dynamic combinations. The difficult part
is to understand how to construct a main segment's series of destroying edges
by dynamic combinations (see the proof of lemma 4). The proof logic is: if
there is at least on Hamilton cycle in the graph, we always can do useful cut
and inserts until a Hamilton cycle is got. The times of useful cut and inserts
are polynomial. So if at any step we cannot have a useful cut and insert, this
means that there are no Hamilton cycles in the graph.Comment: 49 pages. This time, I add a detailed polynomial time algorithm and
proof for 3S
The E3 ubiquitin ligase c-IAP1 regulates PCSK9-mediated LDLR degradation: Linking the TNF-α pathway to cholesterol uptake
Proprotein convertase subtilisin/kexin type 9 (PCSK9), in addition to LDLR (low-density lipoprotein receptor) and APOB (apolipoprotein B), is one of three loci implicated in autosomal dominant hypercholesterolaemia (ADH)^1^. A number of PCSK9 gain-of-function mutations and loss-of-function mutations have been identified from families afflicted with ADH with hypercholesterolaemia or hypocholesterolaemia, respectively^1-4^. In humans, the main function of PCSK9 appears to be the post-transcriptional regulation of the number of cell-surface LDL receptors^5-7^. To date, only LDLR and its closest family members VLDLR and ApoER2 have been shown to bind with PCSK9^8,9^. To find new binding partners for PCSK9, we used a shotgun proteomic method to analyse the protein complex pulled down by immunoprecipitation against FLAG-tagged PCSK9 protein. Among 22 potential novel binding proteins identified, we found that the cellular inhibitor of apoptosis protein 1 (c-IAP1^10^) and the TNF receptor-associated factor 2 (TRAF2^11^) complex are regulated differently in different dominant PCSK9 mutations that occur naturally. Further immunoprecipitation analysis showed that c-IAP1 is a direct binding partner for PCSK9. One of the "gain-of-function" mutants, PCSK9-S127R, which has impaired autocatalytic activity, is defective in binding to c-IAP1. The other dominant mutation, PCSK9-D374Y^12^, which is 10-fold more potent in degrading the LDLR protein than wild-type PCSK9, can be significantly ubiquitinated by c-IAP1 in vitro. The ubiquitinated PCSK9-D374Y is unable to degrade LDLR, which is its main cause of hypercholesterolaemia in patients. These results indicate that there is a novel cholesterol uptake regulation pathway linking PCSK9/LDLR to the E3 ubiquitin ligase c-IAP1 in a TNF-[alpha] response pathway. This highlights the possibility of developing new treatments for human cardiovascular diseases through ubiquitin ligase-mediated ubiquitination of target proteins in cholesterol metabolism
New bounds for circulant Johnson-Lindenstrauss embeddings
This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as
an important class of structured random JL embeddings, are formed by
randomizing the column signs of a circulant matrix generated by a random
vector. With the help of recent decoupling techniques and matrix-valued
Bernstein inequalities, we obtain a new bound
for Gaussian circulant JL embeddings.
Moreover, by using the Laplace transform technique (also called Bernstein's
trick), we extend the result to subgaussian case. The bounds in this paper
offer a small improvement over the current best bounds for Gaussian circulant
JL embeddings for certain parameter regimes and are derived using more direct
methods.Comment: 11 pages; accepted by Communications in Mathematical Science
Crop Yield Prediction Using Deep Neural Networks
Crop yield is a highly complex trait determined by multiple factors such as
genotype, environment, and their interactions. Accurate yield prediction
requires fundamental understanding of the functional relationship between yield
and these interactive factors, and to reveal such relationship requires both
comprehensive datasets and powerful algorithms. In the 2018 Syngenta Crop
Challenge, Syngenta released several large datasets that recorded the genotype
and yield performances of 2,267 maize hybrids planted in 2,247 locations
between 2008 and 2016 and asked participants to predict the yield performance
in 2017. As one of the winning teams, we designed a deep neural network (DNN)
approach that took advantage of state-of-the-art modeling and solution
techniques. Our model was found to have a superior prediction accuracy, with a
root-mean-square-error (RMSE) being 12% of the average yield and 50% of the
standard deviation for the validation dataset using predicted weather data.
With perfect weather data, the RMSE would be reduced to 11% of the average
yield and 46% of the standard deviation. We also performed feature selection
based on the trained DNN model, which successfully decreased the dimension of
the input space without significant drop in the prediction accuracy. Our
computational results suggested that this model significantly outperformed
other popular methods such as Lasso, shallow neural networks (SNN), and
regression tree (RT). The results also revealed that environmental factors had
a greater effect on the crop yield than genotype.Comment: 9 pages, Presented at 2018 INFORMS Conference on Business Analytics
and Operations Research (Baltimore, MD, USA). One of the winning solutions to
the 2018 Syngenta Crop Challeng
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