First passage time for random walks in heterogeneous networks

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.Comment: 5 pages, 3 figure

Exact mean first-passage time on the T-graph

We consider a simple random walk on the T-fractal and we calculate the exact mean time $\tau^g$ to first reach the central node $i_0$. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except $i_0$. By means of analytic techniques based on decimation procedures, we find the explicit expression for $\tau^g$ as a function of the generation $g$ and of the volume $V$ of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.Comment: 6 page

Localization Transition of Biased Random Walks on Random Networks

We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength b_c exists such that most walks find the target within a finite time when b>b_c. For b<b_c, a finite fraction of walks drifts off to infinity before hitting the target. The phase transition at b=b_c is second order, but finite size behavior is complex and does not obey the usual finite size scaling ansatz. By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for b_c and verify it by large scale simulations.Comment: 4 pages, includes 4 figure

Assessment worlds colliding? Negotiating between discourses of assessment on an online open course

Using the badged open course, Taking your first steps into Higher Education, this case study examines how assessment on online open courses draws on concepts of assessment used within formal and informal learning. Our experience was that assessment used within open courses, such as massive open online courses, is primarily determined by the requirements of quality assurance processes to award a digital badge or statement of participation as well as what is technologically possible. However, this disregards much recent work in universities that use assessment in support of learning. We suggest that designers of online open courses should pay greater attention to the relationship of assessment and learning to improve participant course completion

Modeling reactivity to biological macromolecules with a deep multitask network

Most small-molecule drug candidates fail before entering the market, frequently because of unexpected toxicity. Often, toxicity is detected only late in drug development, because many types of toxicities, especially idiosyncratic adverse drug reactions (IADRs), are particularly hard to predict and detect. Moreover, drug-induced liver injury (DILI) is the most frequent reason drugs are withdrawn from the market and causes 50% of acute liver failure cases in the United States. A common mechanism often underlies many types of drug toxicities, including both DILI and IADRs. Drugs are bioactivated by drug-metabolizing enzymes into reactive metabolites, which then conjugate to sites in proteins or DNA to form adducts. DNA adducts are often mutagenic and may alter the reading and copying of genes and their regulatory elements, causing gene dysregulation and even triggering cancer. Similarly, protein adducts can disrupt their normal biological functions and induce harmful immune responses. Unfortunately, reactive metabolites are not reliably detected by experiments, and it is also expensive to test drug candidates for potential to form DNA or protein adducts during the early stages of drug development. In contrast, computational methods have the potential to quickly screen for covalent binding potential, thereby flagging problematic molecules and reducing the total number of necessary experiments. Here, we train a deep convolution neural networkthe XenoSite reactivity modelusing literature data to accurately predict both sites and probability of reactivity for molecules with glutathione, cyanide, protein, and DNA. On the site level, cross-validated predictions had area under the curve (AUC) performances of 89.8% for DNA and 94.4% for protein. Furthermore, the model separated molecules electrophilically reactive with DNA and protein from nonreactive molecules with cross-validated AUC performances of 78.7% and 79.8%, respectively. On both the site- and molecule-level, the model’s performances significantly outperformed reactivity indices derived from quantum simulations that are reported in the literature. Moreover, we developed and applied a selectivity score to assess preferential reactions with the macromolecules as opposed to the common screening traps. For the entire data set of 2803 molecules, this approach yielded totals of 257 (9.2%) and 227 (8.1%) molecules predicted to be reactive only with DNA and protein, respectively, and hence those that would be missed by standard reactivity screening experiments. Site of reactivity data is an underutilized resource that can be used to not only predict if molecules are reactive, but also show where they might be modified to reduce toxicity while retaining efficacy. The XenoSite reactivity model is available at http://swami.wustl.edu/xenosite/p/reactivity

Random Boolean Network Models and the Yeast Transcriptional Network

The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.Comment: 23 pages, 5 figure

Coagulation reaction in low dimensions: Revisiting subdiffusive A+A reactions in one dimension

We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous kinetics'') and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.Comment: The previous version was corrupted - some figures misplaced, some strange words that did not belong. Otherwise identica

Simulations for trapping reactions with subdiffusive traps and subdiffusive particles

While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square displacement $\sim t^\gamma$ with $0<\gamma<1$. Recently we calculated the asymptotic survival probability $P(t)$ of a (sub)diffusive particle ($\gamma^\prime$) surrounded by (sub)diffusive traps ($\gamma$) in one dimension. These are among the few known results for reactions involving species characterized by different anomalous exponents. Our results were obtained by bounding, above and below, the exact survival probability by two other probabilities that are asymptotically identical (except when $\gamma^\prime=1$ and $0<\gamma<2/3$). Using this approach, we were not able to estimate the time of validity of the asymptotic result, nor the way in which the survival probability approaches this regime. Toward this goal, here we present a detailed comparison of the asymptotic results with numerical simulations. In some parameter ranges the asymptotic theory describes the simulation results very well even for relatively short times. However, in other regimes more time is required for the simulation results to approach asymptotic behavior, and we arrive at situations where we are not able to reach asymptotia within our computational means. This is regrettably the case for $\gamma^\prime=1$ and $0<\gamma<2/3$, where we are therefore not able to prove or disprove even conjectures about the asymptotic survival probability of the particle.Comment: 15 pages, 10 figures, submitted to Journal of Physics: Condensed Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin and M.Tachiy

Building a CCD Spectrograph for Educational or Amateur Astronomy

We discuss the design of an inexpensive, high-throughput CCD spectrograph for a small telescope. By using optical fibers to carry the light from the telescope focus to a table-top spectrograph, one can minimize the weight carried by the telescope and simplify the spectrograph design. We recently employed this approach in the construction of IntroSpec, an instrument built for the 16-inch Knowles Telescope on the Harvard College campus.Comment: 17 pages including 7 figures, PASP, accepted (higher resolution figures at http://cfa-www.harvard.edu/~sheila/introspec.ps.gz

Spectral dimensions of hierarchical scale-free networks with shortcuts

The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractals or non-fractals depending on the weight of shortcuts. Applying the renormalization group (RG) approach to the Gaussian model, we obtain the spectral dimension exactly. While the spectral dimension varies between $1$ and $2$ for the fractal case, it remains at $2$, independent of the variation of network structure for the non-fractal case. The crossover behavior between the two cases is studied through the RG flow analysis. The analytic results are confirmed by simulation results and their implications for the architecture of complex systems are discussed.Comment: 10 pages, 3 figure