Graphs Look Research Articles

Prediction of Drug-Drug Interactions by Means of a Graph Look Network Novel Algorithm

Abstract: With the growing need for public health and drug development, combination therapy has become widely used in clinical settings. However, the risk of unexpected adverse effects and unknown toxicity caused by drug-drug interactions (DDIs) is a severe public health issue for polypharmacy safety. Traditional investigational methods for detecting DDIs are expensive and time- consuming. Therefore, many computational methods have been developed in recent years to predict DDIs with the growing availability of data and advancements in artificial intelligence. In silico methods have proven to be effective in predicting DDIs, but detecting potential interactions, especially for newly exposed drugs without an existing DDI network, remains a challenge. In this study, we proposea predicting method of DDIs named HAG-DDI based on graph look networks. We consider the differences in mechanisms between DDIs and add learning of semantic-level attention, which can focus on superior representations of DDIs. By treating interactions as nodes and the presence of the same drug as edges, and constructing small subnetworks during training, we effectively mitigate potential bias issues arising from limited data availability. Our experimental results show that our method achieves an F1-score of 0.952, proving that our model is a viable alternative for DDIs prediction. The codes are available at: https://github.com/xtnenu/DDIFramework.

Large, lengthy graphs look locally like lines

We apply the theory of unimodular random rooted graphs to study the metric geometry of large, finite, bounded degree graphs whose diameter is proportional to their volume. We prove that for a positive proportion of the vertices of such a graph, there exists a mesoscopic scale on which the graph looks like $\mathbb{R}$ in the sense that the rescaled ball is close to a line segment in the Gromov-Hausdorff metric.

Cores of cubelike graphs

A graph is cubelike if it is a Cayley graph for some elementary abelian 2-group Z2n. The core of a graph is its smallest subgraph to which it admits a homomorphism. More than ten years ago, Nešetřil and Šámal (2008) asked whether the core of a cubelike graph is cubelike, but since then very little progress has been made towards resolving the question. Here we investigate the structure of the core of a cubelike graph, deducing a variety of structural, spectral and group-theoretical properties that the core ”inherits” from the host cubelike graph. These properties constrain the structure of the core quite severely — even if the core of a cubelike graph is not actually cubelike, it must bear a very close resemblance to a cubelike graph. Moreover we prove the much stronger result that not only are these properties inherited by the core of a cubelike graph, but also by the orbital graphs of the core. Even though the core and its orbital graphs look very much like cubelike graphs, we are unable to show that this is sufficient to characterize cubelike graphs. However, our results are strong enough to eliminate all non-cubelike graphs on up to 32 vertices as potential cores of cubelike graphs (of any size). Thus, if one exists at all, a cubelike graph with a non-cubelike core has at least 128 vertices and its core has at least 64 vertices.

Adhesion of bacterial cells on carbon supports: characteristics of process and application in biotechnology

The article provides a brief review of methods for studying the process of adhesion of bacterial cells on insoluble abiotic carriers (carbon materials). Determination of the hydrophobicity of microbial cells and the carrier, dispersion, surface roughness of the carrier allows to identify the main patterns of bacterial adhesion on carbon adsorbents. It is shown that the adhered biomass on a hydrophobic carrier is the greater, the higher the hydrophobicity of the cell surface. Correlation analysis showed no reliable relationship between surface roughness, hydrophobicity and dispersion of carriers on the one hand, and the mass of adhered cells on the other hand when considering these characteristics separately, which indicates the need for a comprehensive approach to the assessment of the carrier for immobilizing microbial cells. The mass (amount) of adsorbed cells depends on their concentration in the suspension. The nature of adsorption, subsequently replaced by adhesion, can be described either by the theory of polymolecular adsorption of Brunauer, Emmett, Teller, which implies the formation of a cells polylayer on the surface, or in the case of carrier saturation with cells, the graphs look like Langmuir isotherms. The elemental composition of the carrier has a certain effect on the physiological state of the adhered cells, therefore, it must be taken into account when choosing the optimal carrier of cells in heterogeneous biocatalysis. Scanning electron microscopy allows visualization of adherent cells. Adherent cells of nitrile-hydrolyzing bacteria can be used as biocatalysts for the process of enzymatic transformation of nitriles and amides or in the process of treatment of environment from these toxic substances.

Which subsets of an infinite random graph look random?

AbstractGiven a countable graph, we say a set A of its vertices is universal if it contains every countable graph as an induced subgraph, and A is weakly universal if it contains every finite graph as an induced subgraph. We show that, for almost every graph on , (1) every set of positive upper density is universal, and (2) every set with divergent reciprocal sums is weakly universal. We show that the second result is sharp (i.e., a random graph on will almost surely contain non‐universal sets with divergent reciprocal sums) and, more generally, that neither of these two results holds for a large class of partition regular families.

What Would a Graph Look Like in this Layout? A Machine Learning Approach to Large Graph Visualization.

Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to selecting a good layout is to use aesthetic criteria and visual inspection. However, fully calculating various layouts and their associated aesthetic metrics is computationally expensive. In this paper, we present a machine learning approach to large graph visualization based on computing the topological similarity of graphs using graph kernels. For a given graph, our approach can show what the graph would look like in different layouts and estimate their corresponding aesthetic metrics. An important contribution of our work is the development of a new framework to design graph kernels. Our experimental study shows that our estimation calculation is considerably faster than computing the actual layouts and their aesthetic metrics. Also, our graph kernels outperform the state-of-the-art ones in both time and accuracy. In addition, we conducted a user study to demonstrate that the topological similarity computed with our graph kernel matches perceptual similarity assessed by human users.

Patterns and anomalies in k-cores of real-world graphs with applications

How do the k-core structures of real-world graphs look like? What are the common patterns and the anomalies? How can we exploit them for applications? A k-core is the maximal subgraph in which all vertices have degree at least k. This concept has been applied to such diverse areas as hierarchical structure analysis, graph visualization, and graph clustering. Here, we explore pervasive patterns related to k-cores and emerging in graphs from diverse domains. Our discoveries are: (1) Mirror Pattern: coreness (i.e., maximum k such that each vertex belongs to the k-core) is strongly correlated with degree. (2) Core-Triangle Pattern: degeneracy (i.e., maximum k such that the k-core exists) obeys a 3-to-1 power-law with respect to the count of triangles. (3) Structured Core Pattern: degeneracy–cores are not cliques but have non-trivial structures such as core–periphery and communities. Our algorithmic contributions show the usefulness of these patterns. (1) Core-A, which measures the deviation from Mirror Pattern, successfully spots anomalies in real-world graphs, (2) Core-D, a single-pass streaming algorithm based on Core-Triangle Pattern, accurately estimates degeneracy up to 12 $$\times $$ faster than its competitor. (3) Core-S, inspired by Structured Core Pattern, identifies influential spreaders up to 17 $$\times $$ faster than its competitors with comparable accuracy.

On the asymptotics of constrained exponential random graphs

AbstractThe unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of edges. What does a typical random graph look like, if drawn from an exponential model subject to such constraints? Will there be a similar phase transition phenomenon (as one varies the parameters) as that which occurs in the unconstrained exponential model? We present some general results for this constrained model and then apply them to obtain concrete answers in the edge-triangle model with fixed density of edges.

No Dark Matter? Prediction from Dynamic Universe Model Came True!

This paper discusses about the theoretical “non-requirement” of dark matter, or in other words, there is no missing mass in galaxies. A singularity free and collision free n-body problem solution called dynamic universe model was used to find out the theoretical star circular velocity curves in a galaxy. Here five cases are presented. In the first case a HUGE mass at the center of galaxy, sun like stars and external galaxies are assumed, when plotted, the graph of last iteration shows disk formation and velocities achieved. This circular velocities verses radius graph looks exactly similar to observations by astronomers. In all the other cases, either the central mass is missing or external galaxies are missing or both are missing where resulting graphs look different. It can be inferred that the theoretical requirement of dark matter is calculation error, that no dark matter (missing mass) is required according to dynamic universe model. This prediction was first presented in Tokyo University in 2005. Later the findings from LUX in 2013 the (Large Underground Xenon) experiment confirmed this prediction. This new Tensor math in dynamic universe model was used for solving a large variety of physical problems which are otherwise not possible with present day physics. This method solved many unsolved problems earlier like existence of blue shifted galaxies galaxy disk formations, missing mass in galaxies, pioneer anomaly, non-collapsing large scale mass structures and new horizons trajectory predictions etc. AMS subject classifications: 70F10 (n-body problems), 70F15 (celestial mechanics), 70E55 (dynamics of multi body systems) 70-05 (experimental work) 70-08 (computational methods).

Computing and counting longest paths on circular-arc graphs in polynomial time

The longest path problem asks for a path with the largest number of vertices in a given graph. In contrast to the Hamiltonian path problem, until recently polynomial algorithms for the longest path problem were known only for small graph classes, such as trees. Recently, a polynomial algorithm for this problem on interval graphs has been presented in Ioannidou et al. (2011) [19] with running time O(n4) on a graph with n vertices, thus answering the open question posed in Uehara and Uno (2004) [32]. Even though interval and circular-arc graphs look superficially similar, they differ substantially, as circular-arc graphs are not perfect; for instance, several problems– e.g. coloring –are NP-hard on circular-arc graphs, although they can be efficiently solved on interval graphs. In this paper, we prove that for every path P of a circular-arc graph G, we can appropriately “cut” the circle, such that the obtained (not induced) interval subgraph G′ of G admits a path P′ on the same vertices as P. This non-trivial result is of independent interest, as it suggests a generic reduction of a number of path problems on circular-arc graphs to the case of interval graphs with a multiplicative linear time overhead of O(n). As an application of this reduction, we present the first polynomial algorithm for the longest path problem on circular-arc graphs. In addition, by exploiting deeper the structure of circular-arc graphs, we manage to get rid of the linear time overhead of the reduction, and thus this algorithm turns out to have the same running time O(n4) as the one on interval graphs. Our algorithm, which significantly simplifies the approach of Ioannidou et al. (2011) [19], computes in the same time an n-approximation of the (exponentially large in worst case) number of different vertex sets that provide a longest path; in the case where G is an interval graph, we compute the exact number. Moreover, in contrast to Ioannidou et al. (2011) [19], this algorithm can be directly extended with the same running time to the case where every vertex has an arbitrary positive weight.

Computing and Counting Longest Paths on Circular-Arc Graphs in Polynomial Time

The longest path problem asks for a path with the largest number of vertices in a given graph. The first polynomial time algorithm (with running time O(n4)) has been recently developed for interval graphs. Even though interval and circular-arc graphs look superficially similar, they differ substantially, as circular-arc graphs are not perfect. In this paper, we prove that for every path P of a circular-arc graph G, we can appropriately “cut” the circle, such that the obtained (not induced) interval subgraph G′ of G admits a path P′ on the same vertices as P. This non-trivial result is of independent interest, as it suggests a generic reduction of a number of path problems on circular-arc graphs to the case of interval graphs with a multiplicative linear time overhead of O(n). As an application of this reduction, we present the first polynomial algorithm for the longest path problem on circular-arc graphs, which turns out to have the same running time O(n4) with the one on interval graphs, as we manage to get rid of the linear overhead of the reduction. This algorithm computes in the same time an n-approximation of the number of different vertex sets that provide a longest path; in the case where G is an interval graph, we compute the exact number. Moreover, our algorithm can be directly extended with the same running time to the case where every vertex has an arbitrary positive weight.

The large deviation principle for the Erdős-Rényi random graph

What does an Erdős-Rényi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and proof of the main result uses the recent development of the theory of graph limits by Lovász and coauthors and Szemerédi’s regularity lemma from graph theory. As a basic application of the general principle, we work out large deviations for the number of triangles in G ( n , p ) . Surprisingly, even this simple example yields an interesting double phase transition.

The Four-in-a-Tree Problem in Triangle-Free Graphs

The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time O(n 4) whether three given vertices of a graph belong to an induced tree. Here, we study four-in- a-tree for triangle-free graphs. We give a structural answer to the following question: what does a triangle-free graph look like if no induced tree covers four given vertices? Our main result says that any such graph must have the “same structure”, in a sense to be defined precisely, as a square or a cube. We provide an O(nm)-time algorithm that given a triangle-free graph G together with four vertices outputs either an induced tree that contains them or a partition of V(G) certifying that no such tree exists. We prove that the problem of deciding whether there exists a tree T covering the four vertices such that at most one vertex of T has degree at least 3 is NP-complete.

Teaching Bayes to Graduate Students in Political Science, Sociology, Public Health, Education, Economics, …

I was trying to draw Bert and Ernie the other day, and it was really difficult. I had pictures of them right next to me, but my drawings were just incredibly crude, more linguistic than vi sual in the sense that I was portraying key aspects of Bert and Ernie but in pictures that didn't look anything like them. I know that drawing is difficult?every once in awhile, I sit for an hour to draw a scene, and it's always a lot of work to get it to look anything like what I'm seeing?but I didn't realize it would be so hard to draw cartoon characters] This got me to thinking about the students in my statistics classes. When I ask them to sketch a scatterplot of data, or to plot some function, they can never draw a realistic-looking pic ture. Their density functions don't go to zero in the tails, the scatter in their scatterplots does not match their standard devia tions, E(y\x) does not equal their regression line, and so forth. For example, when asked to draw a potential scatterplot of earn ings versus height, they have difficulty with the x-axis (most people are between 60 and 75 inches in height) and having the data consistent with the regression line, while having all earn ings be nonnegative. (Yes, it's better to model on the log scale or whatever, but that's not the point of this exercise.) Anyway, the students just can't make these graphs look right, which has always frustrated me. But my Bert and Ernie expe rience suggests that I'm thinking of it the wrong way. Maybe they need lots and lots of practice before they can draw realistic functions and scatterplots. They'll certainly need lots of practice to learn Bayesian methods.

Casualties of Reform

IN ALL the debate about what it will take to realize the grand promises of No Child Left Behind, we've somehow managed to miss the most important truth: it isn't going to work no matter how much money we feed it. The principles that drive NCLB are fundamentally flawed, and though it might achieve some good in the Third World conditions of our nation's worst schools, in places accustomed to success, performance levels will inevitably decline as all concerned discover that mediocrity has become the new excellence. This is a lesson we're learning the hard way here in New York, where our own school reform program, now nearly a decade old, not only embraces the same core principles as NCLB but even goes the feds one better. Not content to simply leave no New York child behind, we are holding each of them to new, higher standards in the process. In fact, when our reform bears full fruit--when all our high school students can pass the Regents Exams with a score of at least 65%--we will have honored the reformers' pledge to raise the bar for all our students. That's the official word, and by all official accounts the process is going splendidly. Test scores are up. The charts and graphs look good. Best of all, advocates for this test-them-till-they-bleed approach say the numbers the testing is generating are finally imposing accountability on an unruly system. But that's not how it looks down here in the classroom. What we see in practice are not higher standards, but lower standards. They're not lower for everybody all the time, but they're lower for such a large and significant portion of the population that it seems fair simply to say they're lower. And now, for growing numbers of teachers, particularly the older and crankier among us, our new, higher standards--a phrase difficult even to utter without first spitting on the ground--have many of us, sadly and for the first time, looking for the exit sign. And while that last bit of news might strike ardent teacher-bashers as an indication that the program is succeeding, even they should be able to appreciate the one special qualification that veteran teachers bring to the table when the subject is reform. Nobody has been reformed more than we have. We are the real experts in the field. Over the years we've been retrained, newly sensitized, paradigmatically shifted, and whatever else so much that many of us no longer even recognize this as the job we were originally hired to do. To us, the recent history of public education reads like a study in the grotesque distortions that can be wrought on a system subjected to endless helpings of well-intended expertise. In fact, those of us who were around two and three decades ago lived through the golden age of school reform, when the coming of each new year was marked by the annual Rites of Autumn: opening day and the ritual unveiling of that year's plan to rescue public education. In those heady days, legions of competing theorists angled for the grand prize, the opportunity to treat our classrooms as their real-life laboratories. Over the years, we've seen a great many of these beauties come and go--and sometimes even come back again, the second time with a new name and sponsor. Yet of all those well-intended failures, none can top this current crop for sheer destructive potential, no small claim in a system that's produced some truly memorable stinkers. Remember the self-esteem movement? Surely it was never meant to spawn a generation with such a disproportionate number of frightening young egotists, but it did. And nobody meant for the noble intentions of the special education reformers to evolve into a nightmare of expense and bureaucratic excess. But that happened too. We didn't bring that nonsense to the schoolhouse; we endured it. But our endurance was not without resistance. In truth, forced participation in those and so many other assaults on good sense inspired in many of us a long stealth campaign of mitigating the harm done by the worst such plans by simply ignoring them in the classroom while speaking of them to officials and in the correct jargon of the moment. …

Obliquely propagating large amplitude solitary waves in charge neutral plasmas

Abstract. This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons) cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not) of the phase, since the amplitude or envelope graphs look very similar.

Uncertainty relations expressed by Shannon-like entropies

Abstract Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

Tips for Readers of Research: ‘Seeing Through’ the Graphs

IN SEVERAL books, I have encouraged readers to graphs. To see through a graph is to ignore the picture and ascertain the meaning. A picture might be worth a thousand words, but pictures also lie on occasion. More often, they simply mislead. In the November 2002 issue of the NCTM News Bulletin, Johnny Lott, president of the National Council of Teachers of Mathematics, takes Brookings Institution fellow Tom Loveless to task for using misleading graphs concerning improvements on the NAEP mathematics assessments. The graphs appear in the Brookings publication The 2002 Brown Center Report on American Education: How Well Are American Students Learning? Lott begins by invoking the statistician's bible of sarcasm: Darrell Huff's 1954 How to Lie with Statistics, which is still in print. One way of making a graph look more impressive, Huff advised, is to change the proportion between the units used for the ordinate (vertical axis) and abscissa (horizontal axis). Lott accuses Loveless of using this deception, which is shown in Figure 1. The first points designating the NAEP (National Assessment of Educational Progress) testing years are two years apart -- 1990 and 1992 -- while the other two are four years apart -- 1996 and 2000. Yet the space of all three intervals is represented as the same. Loveless should have made the distance between 1990 and 1992 half the size of the distances between 1992 and 1996 and 1996 and 2000. In correcting Loveless, though, it seems to me that Lott has created a graph that is just as arbitrary as the original one -- and perhaps even more misleading. Lott converts Loveless' rectangles to squares, with each point between squares on the abscissa representing two years and each point between squares on the ordinate representing two points of the NAEP scale. Lott's version is shown in Figure 2. Lott claims that this is a more honest graph, and it does fix the problem of unequal intervals on the abscissa. But the choice of how to proportion the units in this case (and for most any graph) is arbitrary. Certainly there is nothing inherently meaningful in plotting every two NAEP points. We could plot every single NAEP point or every fifth NAEP point with equal justification. Similarly, there is no theoretical justification whatsoever for making the space between two points on the NAEP scale equal in size to two years of time, but that's what Lott's squares do. I repeat: the choice of proportions is arbitrary, not in the sense of being capricious but in the sense that judgment is required. If the two graphs represented rising costs of something and if you were a superintendent, you might choose one or the other depending on the message you wished to convey to your school board. Moreover, the gains are the same in both graphs. They show changes in average scores over time. The honesty -- or at least the meaningfulness -- of both graphs would be greatly improved by an indication of the variability of the scores around these averages. Remember from basic statistics: No measure of central tendency without a measure of dispersion. The scores rise from 213 in 1990 to 228 in 2000. Is this a meaningful gain? An important gain? Given what psychometricians have been saying lately about the volatility of test scores, we might also ask whether the gain is due mostly to chance or to factors that have nothing to do with the quality of instruction. We would interpret the gains differently if 228 were a full standard deviation above 213 or only one-fourth of a standard deviation above. We can't tell from the graphs. If we knew what the standard deviation was, we could calculate an effect size, a statistic that leads more to practical interpretations than does a calculation of whether or not the gain is statistically significant. …

Geometry and Diameter Bounds of Directed Cayley Graphs of Abelian Groups

Many popular interconnection network topologies, such as hypercubes and toroidal meshes, are based on Cayley graphs of Abelian groups. The symmetry and algebraic structure of these graphs result in many nice physical properties of the network concerning layout, routing algorithms, and load balancing. There has been interest in low-diameter Abelian--Cayley graphs because of their smaller communication delay and reduced congestion. For any fixed number of nodes n, and any fixed out-degree k, we are interested in how small the diameter of directed Cayley graphs of Abelian groups can be and what these low-diameter graphs look like. We give an upper bound of $n \leq \frac{3(d + 3)^3}{25}$ for the size of directed Abelian--Cayley graphs with k = 3 and diameter d, correcting a previously published result by Hsu and Jia [SIAM J. Discrete Math., 7 (1994), pp. 57--71]. Our method is based on translational tiling techniques and is a generalization of Wong and Coppersmith's method for k = 2 [J. Assoc. Comput. Mach., 21 (1974), pp. 392--402]. Moreover, our method works for all Abelian groups, not just the cyclic case. For k = 3 we give computational results for the largest Abelian--Cayley graph as a function of diameter. When n = 84 m3 , for integer m, there is a network with $n = \frac{(d + 3)^3}{11.95}$ whose diameter is approximately three-fourths of that of a three-dimensional toroidal cube.

Coupling of multiple q-state Potts models to 2 d gravity

Monte Carlo simulations are used to investigate the coupling of multiple q-state Potts models ( q = 2, 3 and 4) to 2 d gravity. We see in the weak non-magnetized phase of the spin models a strong coupling between the spins and gravity and that the strength of this coupling seems to depend only on the central charge c. And for sufficiently high values of c the graphs look like branched polymers. But at the phase transition the spin models decouple from gravity and in the magnetized phase the geometry returns to that of pure gravity.