Ordered Navigation on Multi-attributed Data Words

We study temporal logics and automata on multi-attributed data words. Recently, BD-LTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt. tuples of data values renders the logic undecidable, we introduce ND-LTL, an extension of BD-LTL by a restricted form of tuple-navigation. While complete ND-LTL is still undecidable, the two natural fragments allowing for either future or past navigation along data values are shown to be Ackermann-hard, yet decidability is obtained by reduction to nested multi-counter systems. To this end, we introduce and study nested variants of data automata as an intermediate model simplifying the constructions. To complement these results we show that imposing the same restrictions on BD-LTL yields two 2ExpSpace-complete fragments while satisfiability for the full logic is known to be as hard as reachability in Petri nets

Greedy low-rank algorithm for spatial connectome regression

Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regression problem (Harris et al., 2016), but existing techniques do not scale to the whole-brain setting. The corresponding matrix equation is challenging to solve due to large scale, ill-conditioning, and a general form that lacks a convergent splitting. We propose a greedy low-rank algorithm for connectome reconstruction problem in very high dimensions. The algorithm approximates the solution by a sequence of rank-one updates which exploit the sparse and positive definite problem structure. This algorithm was described previously (Kressner and Sirkovi\'c, 2015) but never implemented for this connectome problem, leading to a number of challenges. We have had to design judicious stopping criteria and employ efficient solvers for the three main sub-problems of the algorithm, including an efficient GPU implementation that alleviates the main bottleneck for large datasets. The performance of the method is evaluated on three examples: an artificial "toy" dataset and two whole-cortex instances using data from the Allen Mouse Brain Connectivity Atlas. We find that the method is significantly faster than previous methods and that moderate ranks offer good approximation. This speedup allows for the estimation of increasingly large-scale connectomes across taxa as these data become available from tracing experiments. The data and code are available online

Direct, physically-motivated derivation of the contagion condition for spreading processes on generalized random networks

For a broad range single-seed contagion processes acting on generalized random networks, we derive a unifying analytic expression for the possibility of global spreading events in a straightforward, physically intuitive fashion. Our reasoning lays bare a direct mechanical understanding of an archetypal spreading phenomena that is not evident in circuitous extant mathematical approaches.Comment: 4 pages, 1 figure, 1 tabl

What do we know about succession in family businesses? Mapping current knowledge and unexplored territory

We review studies on succession in family businesses that have been done since Handler’s (1994) seminal literature review on the topic in an effort to synthesize existing research and outline paths for future studies. We offer three contributions. First, we select succession studies that adhere to established methodological standards. Second, we review these studies based on the perspective that succession is a process comprising five stages across three levels of analysis. Finally, we outline current gaps in our knowledge and ask researchers to adopt a more holistic approach when studying succession

Exact solutions for social and biological contagion models on mixed directed and undirected, degree-correlated random networks

We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree-degree correlations. Our work extends previous theoretical developments for the undirected case, and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed-form expressions.Comment: 10 pages, 3 figure

Patterns driven by combined AC and DC electric fields in nematic liquid crystals

The effect of superimposed ac and dc electric fields on the formation of electroconvection and flexoelectric patterns in nematic liquid crystals was studied. For selected ac frequencies an extended standard model of the electro-hydrodynamic instabilities was used to characterize the onset of pattern formation in the two-dimensional parameter space of the magnitudes of the ac and dc electric field components. Numerical as well as approximate analytical calculations demonstrate that depending on the type of patterns and on the ac frequency, the combined action of ac and dc fields may either enhance or suppress the formation of patterns. The theoretical predictions are qualitatively confirmed by experiments in most cases. Some discrepancies, however, seem to indicate the need to extend the theoretical description

Twitter reciprocal reply networks exhibit assortativity with respect to happiness

The advent of social media has provided an extraordinary, if imperfect, 'big data' window into the form and evolution of social networks. Based on nearly 40 million message pairs posted to Twitter between September 2008 and February 2009, we construct and examine the revealed social network structure and dynamics over the time scales of days, weeks, and months. At the level of user behavior, we employ our recently developed hedonometric analysis methods to investigate patterns of sentiment expression. We find users' average happiness scores to be positively and significantly correlated with those of users one, two, and three links away. We strengthen our analysis by proposing and using a null model to test the effect of network topology on the assortativity of happiness. We also find evidence that more well connected users write happier status updates, with a transition occurring around Dunbar's number. More generally, our work provides evidence of a social sub-network structure within Twitter and raises several methodological points of interest with regard to social network reconstructions.Comment: 22 pages, 21 figures, 5 tables, In press at the Journal of Computational Scienc

Polynomial time quantum algorithms for certain bivariate hidden polynomial problems

We present a new method for solving the hidden polynomial graph problem (HPGP) which is a special case of the hidden polynomial problem (HPP). The new approach yields an efficient quantum algorithm for the bivariate HPGP even when the input consists of several level set superpositions, a more difficult version of the problem than the one where the input is given by an oracle. For constant degree, the algorithm is polylogarithmic in the size of the base field. We also apply the results to give an efficient quantum algorithm for the oracle version of the HPP for an interesting family of bivariate hidden functions. This family includes diagonal quadratic forms and elliptic curves.Comment: Theorem numbering changed; new subsection with a high-level description of the main algorith

Temporal patterns of happiness and information in a global social network: Hedonometrics and Twitter

Individual happiness is a fundamental societal metric. Normally measured through self-report, happiness has often been indirectly characterized and overshadowed by more readily quantifiable economic indicators such as gross domestic product. Here, we examine expressions made on the online, global microblog and social networking service Twitter, uncovering and explaining temporal variations in happiness and information levels over timescales ranging from hours to years. Our data set comprises over 46 billion words contained in nearly 4.6 billion expressions posted over a 33 month span by over 63 million unique users. In measuring happiness, we use a real-time, remote-sensing, non-invasive, text-based approach---a kind of hedonometer. In building our metric, made available with this paper, we conducted a survey to obtain happiness evaluations of over 10,000 individual words, representing a tenfold size improvement over similar existing word sets. Rather than being ad hoc, our word list is chosen solely by frequency of usage and we show how a highly robust metric can be constructed and defended.Comment: 27 pages, 17 figures, 3 tables. Supplementary Information: 1 table, 52 figure