Balanced configurations of points in the plane

A balanced configuration of points on the sphere $S^2$ is a (finite) set of points which are in equilibrium if they act on each other according any force law dependent only on the distance between two points. The configuration is additionally group-balanced if for each point in a configuration $\mathcal{C}$, there is a symmetry of $\mathcal{C}$ fixing only that point and its antipode. Leech showed that these definitions are equivalent on the sphere $S^2$ by classifying all possible balanced configurations. On the other hand, Cohn, Elkies, Kumar, and Sch\"urmann showed that for $n\geq 7,$ there are examples of balanced configurations in $S^{n-1}$ which are not group balanced. They also suggested extending the notion of balanced configurations to Euclidean space, and conjectured that at least in the case of the plane, all discrete balanced configurations in $\mathbb{R}^n$ are group-balanced. We verify a reformulation of this conjecture by providing a complete classification of the balanced configurations in $\mathbb{R}^2$ satisfying a certain minimal distance property.Comment: 22 pages, 23 figure

Vertebrate DNA damage tolerance requires the C-terminus but not BRCT or transferase domains of REV1

REV1 is central to the DNA damage response of eukaryotes through an as yet poorly understood role in translesion synthesis. REV1 is a member of the Y-type DNA polymerase family and is capable of in vitro deoxycytidyl transferase activity opposite a range of damaged bases. However, non-catalytic roles for REV1 have been suggested by the Saccharomyces cerevisiae rev1-1 mutant, which carries a point mutation in the N-terminal BRCT domain, and the recently demonstrated ability of the mammalian protein to interact with each of the other translesion polymerases via its extreme C-terminus. Here, we show that a region adjacent to this polymerase interacting domain mediates an interaction with PCNA. These C-terminal domains of REV1 are necessary, although not sufficient, for effective tolerance of DNA damage in the avian cell line DT40, while the BRCT domain and transferase activity are not directly required. Together these data provide strong support for REV1 playing an important non-catalytic role in coordinating translesion synthesis. Further, unlike in budding yeast, rad18 is not epistatic to rev1 for DNA damage tolerance suggesting that REV1 and RAD18 play largely independent roles in the control of vertebrate translesion synthesis

Automated Sensitivity Analysis for Probabilistic Loops

We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from symbolic computation, probability theory, and static analysis in order to automatically capture sensitivity information about probabilistic loops. Sensitivity information allows us to formally establish how value distributions of probabilistic loop variables influence the functional behavior of loops, which can in particular be helpful when choosing values of loop variables in order to ensure efficient/expected computations. Our work uses algebraic techniques to model higher moments of loop variables via linear recurrence equations and introduce the notion of sensitivity recurrences. We show that sensitivity recurrences precisely model loop sensitivities, even in cases where the moments of loop variables do not satisfy a system of linear recurrences. As such, we enlarge the class of probabilistic loops for which sensitivity analysis was so far feasible. We demonstrate the success of our approach while analyzing the sensitivities of probabilistic loops

Assessing the impact of long term frozen storage of faecal samples on protein concentration and protease activity

The proteome is the second axis of the microbiome:host interactome and proteases are a significant aspect in this interaction. They interact with a large variety of host proteins and structures and in many situations are implicated in pathogenesis. Furthermore faecal samples are commonly collected and stored frozen so they can be analysed at a later date. So we were interested to know whether long term storage affected the integrity of proteases and total protein and whether historical native faecal samples were still a viable option for answering research questions around the functional proteome

Strong Invariants Are Hard: On the Hardness of Strongest Polynomial Invariants for (Probabilistic) Programs

We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the strongest polynomial invariants are computable for affine loops, for polynomial loops the problem remained wide open. As an intermediate result of independent interest, we prove that reachability for discrete polynomial dynamical systems is Skolem-hard as well. Furthermore, we generalize the notion of invariant ideals and introduce moment invariant ideals for probabilistic programs. With this tool, we further show that the strongest polynomial moment invariant is (i) uncomputable, for probabilistic loops with branching statements, and (ii) Skolem-hard to compute for polynomial probabilistic loops without branching statements. Finally, we identify a class of probabilistic loops for which the strongest polynomial moment invariant is computable and provide an algorithm for it

The Yin-Yang dataset

The Yin-Yang dataset was developed for research on biologically plausible error backpropagation and deep learning in spiking neural networks. It serves as an alternative to classic deep learning datasets, especially in early-stage prototyping scenarios for both network models and hardware platforms, for which it provides several advantages. First, it is smaller and therefore faster to learn, thereby being better suited for small-scale exploratory studies in both software simulations and hardware prototypes. Second, it exhibits a very clear gap between the accuracies achievable using shallow as compared to deep neural networks. Third, it is easily transferable between spatial and temporal input domains, making it interesting for different types of classification scenarios