As the length of molecular dynamics (MD) trajectories grows with increasing computational power, so does the importance of clustering methods for partitioning trajectories into conformational bins. Of the methods available, the vast majority require users to either have some a priori knowledge about the system to be clustered or to tune clustering parameters through trial and error. Here we present non-parametric uses of two modern clustering techniques suitable for first-pass investigation of an MD trajectory. Being non-parametric, these methods require neither prior knowledge nor parameter tuning. The first method, HDBSCAN, is fast—relative to other popular clustering methods—and is able to group unstructured or intrinsically disordered systems (such as intrinsically disordered proteins, or IDPs) into bins that represent global conformational shifts. HDBSCAN is also useful for determining the overall stability of a system—as it tends to group stable systems into one or two bins—and identifying transition events between metastable states. The second method, iMWK-Means, with explicit rescaling followed by K-Means, while slower than HDBSCAN, performs well with stable, structured systems such as folded proteins and is able to identify higher resolution details such as changes in relative position of secondary structural elements. Used in conjunction, these clustering methods allow a user to discern quickly and without prior knowledge the stability of a simulated system and identify both local and global conformational changes.

Address shuffling is a type of moving target defense that prevents an attacker from reliably contacting a system by periodically remapping network addresses. Although limited testing has demonstrated it to be effective, little research has been conducted to examine the theoretical limits of address shuffling. As a result, it is difficult to understand how effective shuffling is and under what circumstances it is a viable moving target defense. This paper introduces probabilistic models that can provide insight into the performance of address shuffling. These models quantify the probability of attacker success in terms of network size, quantity of addresses scanned, quantity of vulnerable systems, and the frequency of shuffling. Theoretical analysis shows that shuffling is an acceptable defense if there is a small population of vulnerable systems within a large network address space, however shuffling has a cost for legitimate users. These results will also be shown empirically using simulation and actual traffic traces.

Hall (2000) has described zero‐inflated Poisson and binomial regression models that include random effects to account for excess zeros and additional sources of heterogeneity in the data. The authors of the present paper propose a general score test for the null hypothesis that variance components associated with these random effects are zero. For a zero‐inflated Poisson model with random intercept, the new test reduces to an alternative to the overdispersion test of Ridout, Demério & Hinde (2001). The authors also examine their general test in the special case of the zero‐inflated binomial model with random intercept and propose an overdispersion test in that context which is based on a beta‐binomial alternative.

Abstract. This paper studies the behavior of positive solutions of the recursive equationwith y −s , y −s+1 , . . . , y −1 ∈ (0, ∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = max{k, m}. We prove that if gcd(k, m) = 1, with k odd, then y n tends to 2, exponentially. When combined with a recent result of E.

Community structure, including relationships between and within groups, is foundational to our understanding of the world around us. For dissimilarity-based data, leveraging social concepts of conflict and alignment, we provide an approach for capturing meaningful structural information resulting from induced local comparisons. In particular, a measure of local (community) depth is introduced that leads directly to a probabilistic partitioning conveying locally interpreted closeness (or cohesion). A universal choice of threshold for distinguishing strongly and weakly cohesive pairs permits consideration of both local and global structure. Cases in which one might benefit from use of the approach include data with varying density such as that arising as snapshots of complex processes in which differing mechanisms drive evolution locally. The inherent recalibrating in response to density allows one to sidestep the need for localizing parameters, common to many existing methods. Mathematical results together with applications in linguistics, cultural psychology, and genetics, as well as to benchmark clustering data have been included. Together, these demonstrate how meaningful community structure can be identified without additional inputs (e.g., number of clusters or neighborhood size), optimization criteria, iterative procedures, or distributional assumptions.