Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

Select, Link and Rank: Diversified Query Expansion and Entity Ranking using Wikipedia

A search query, being a very concise grounding of user intent, could potentially have many possible interpretations. Search engines hedge their bets by diversifying top results to cover multiple such possibilities so that the user is likely to be satisfied, whatever be her intended interpretation. Diversified Query Expansion is the problem of diversifying query expansion suggestions, so that the user can specialize the query to better suit her intent, even before perusing search results. We propose a method, Select-Link-Rank, that exploits semantic information from Wikipedia to generate diversified query expansions. SLR does collective processing of terms and Wikipedia entities in an integrated framework, simultaneously diversifying query expansions and entity recommendations. SLR starts with selecting informative terms from search results of the initial query, links them to Wikipedia entities, performs a diversity-conscious entity scoring and transfers such scoring to the term space to arrive at query expansion suggestions. Through an extensive empirical analysis and user study, we show that our method outperforms the state-of-the-art diversified query expansion and diversified entity recommendation techniques.

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity.

Recent evidence has highlighted the important role that number ordering skills play in arithmetic abilities (e.g., Lyons & Beilock, 2011). In fact, Lyons et al. (2014) demonstrated that although at the start of formal mathematics education number comparison skills are the best predictors of arithmetic performance, from around the age of 10, number ordering skills become the strongest numerical predictors of arithmetic abilities. In the current study we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was partially mediated by number ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor which included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

A Microbial Link to Weathering of Postglacial Rocks and Sediments, Mount Viso Area, Western Alps, Demonstrated through Analysis of a Soil/Paleosol Bio/Chronosequence

Understanding the mechanism associated with rates of weathering and evolution of rocks→sediment→soil→paleosol in alpine environments raises questions related to the impact of microbial mediation versus various diverse abiotic chemical/physical processes, even including the overall effect of cosmic impact/airburst during the early stage of weathering in Late Glacial (LG) deposits. This study is of a chronosequence of soils/paleosols, with an age range that spans the post–Little Ice Age (post-LIA; <150 yr), the Little Ice Age (LIA; AD 1500–1850), the middle Neoglacial (∼3 ka)–Younger Dryas (YD; <12.8 ka), and the LG (<15 ka). The goal is to elicit trends in weathering, soil morphogenesis, and related eubacterial population changes over the past 13–15 k.yr. The older LG/YD paleosols in the sequence represent soil morphogenesis that started during the closing stage of Pleistocene glaciation. These are compared with undated soils of midto late Neoglacial age, the youngest of LIA and post-LIA age. All profiles formed in a uniform parentmaterial ofmetabasalt composition and in moraine, rockfall, protalus, and alluvial fan deposits. Elsewhere in Europe,North America, and Asia, the cosmic impact/airburst event at 12.8 ka often produced a distinctive, carbon-rich “black mat” layer that shows evidence of high-temperature melting. At this alpine site, older profiles of similar LG age contain scorched and melted surface sediments that are otherwise similar in composition to the youngest/thinnest profiles developing in the catchment today. Moreover, microbial analysis of the sediments offers new insight into the genesis of these sediments: the C and Cu (u = unweathered) horizons in LG profiles present at 12.8 ka (now Ah/Bw) show bacterial population structures that differ markedly from recent alluvial/protalus sample bacterial populations. We propose here that these differences are, in part, a direct consequence of the age/cosmic impact/weathering processes that have occurred in the chronosequence. Of the several questions that emerge from these sequences, perhaps the most important involve the interaction of biotic-mineral factors, which need to be understood if we are to generally fully appreciate the role played by microbes in rock weathering.