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Szalkai B.,Eotvos Lorand University | Varga B.,Eotvos Lorand University | Grolmusz V.,Eotvos Lorand University | Grolmusz V.,Uratim Ltd.
PLoS ONE | Year: 2015

Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph. We have also found that the minimum bisection width, normalized with the edge number, is also significantly larger in the right and the left hemispheres in females: therefore, the differing bisection widths are independent from the difference in the number of edges. © 2015 Szalkai et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Source


Kerepesi C.,Eotvos Lorand University | Grolmusz V.,Eotvos Lorand University | Grolmusz V.,Uratim Ltd.
Archives of Virology | Year: 2016

The Kutch Desert (Great Rann of Kutch, Gujarat, India) is a unique ecosystem: in the larger part of the year it is a hot, salty desert that is flooded regularly in the Indian monsoon season. In the dry season, the crystallized salt deposits form the “white desert” in large regions. The first metagenomic analysis of the soil samples of Kutch was published in 2013, and the data were deposited in the NCBI Sequence Read Archive. At the same time, the sequences were analyzed phylogenetically for prokaryotes, especially for bacteria. In the present work, we identified DNA sequences of recently discovered giant viruses in the soil samples from the Kutch Desert. Since most giant viruses have been discovered in biofilms in industrial cooling towers, ocean water, and freshwater ponds, we were surprised to find their DNA sequences in soil samples from a seasonally very hot and arid, salty environment. © 2015, Springer-Verlag Wien. Source


Szalkai B.,Eotvos Lorand University | Grolmusz V.,Eotvos Lorand University | Grolmusz V.,Uratim Ltd.
Biochimica et Biophysica Acta - General Subjects | Year: 2016

Background: Metagenomic analysis of environmental and clinical samples is gaining considerable importance in today's literature. Changes in the composition of the intestinal microbial communities, relative to the healthy control, are reported in numerous conditions. Methods: We have carefully analyzed the frequencies of the short nucleotide sequences in the metagenomes of two different enterotypes; namely of Chinese and European origins. Results: We have identified 255 nucleotide sequences of length up to 9, such that their frequencies significantly differ in the two enterotypes examined. Conclusions: We have demonstrated that short nucleotide sequences are capable of differentiating enterotypes, and not only metagenomes, originating from healthy and diseased subjects. General significance: Our results may imply that the frequency-differences of certain short nucleotides have diagnostical value if properly applied for different clusters of metagenomes. © 2016 Elsevier B.V. Source


Grolmusz V.,Eotvos Lorand University | Grolmusz V.,Uratim Ltd.
Information Processing Letters | Year: 2015

The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the literature it is widely - but not exclusively - noted that the PageRank for undirected graphs is proportional to the degrees of the vertices of the graph. We prove that statement for a particular personalization vector in the definition of the PageRank, and we also show that in general, the PageRank of an undirected graph is not exactly proportional to the degree distribution of the graph: our main theorem gives an upper and a lower bound to the l1 norm of the difference of the PageRank and the degree distribution vectors. A necessary and sufficient condition is also given for the PageRank for being proportional to the degree. © 2015 Elsevier B.V. Allrightsreserved. Source


Szalkai B.,Eotvos Lorand University | Grolmusz V.,Eotvos Lorand University | Grolmusz V.,Uratim Ltd.
Genomics | Year: 2016

Discoveries of new biomarkers for frequently occurring diseases are of special importance in today's medicine. While fully developed type II diabetes (T2D) can be detected easily, the early identification of high risk individuals is an area of interest in T2D, too. Metagenomic analysis of the human bacterial flora has shown subtle changes in diabetic patients, but no specific microbes are known to cause or promote the disease. Moderate changes were also detected in the microbial gene composition of the metagenomes of diabetic patients, but again, no specific gene was found that is present in disease-related and missing in healthy metagenome. However, these fine differences in microbial taxon- and gene composition are difficult to apply as quantitative biomarkers for diagnosing or predicting type II diabetes. In the present work we report some nucleotide 9-mers with significantly differing frequencies in diabetic and healthy intestinal flora. To our knowledge, it is the first time such short DNA fragments have been associated with T2D. The automated, quantitative analysis of the frequencies of short nucleotide sequences seems to be more feasible than accurate phylogenetic and functional analysis, and thus it might be a promising direction of diagnostic research. © 2016 Elsevier Inc. Source

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