Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

A reconstructed Siberian High index since A. D. 1599 from Eurasian and North American tree rings

The long-term variability of the Siberian High, the dominant Northern Hemisphere anticyclone during winter, is largely unknown. To investigate how this feature varied prior to the instrumental record, we present a reconstruction of a Dec-Feb Siberian High (SH) index based on Eurasian and North American tree rings. Spanning 1599-1980, it provides information on SH variability over the past four centuries. A decline in the instrumental SH index since the late 1970s, related to Eurasian warming, is the most striking feature over the past four hundred years. It is associated with a highly significant (p < 0.0001) step change in 1989. Significant similar to 3-4 yr spectral peaks in the reconstruction fall within the range of variability of the East Asian winter monsoon (which has also declined recently) and lend further support to proposed relationships between these largescale features of the climate system.

Parallel Monte Carlo algorithms for information retrieval

In any data mining applications, automated text and text and image retrieval of information is needed. This becomes essential with the growth of the Internet and digital libraries. Our approach is based on the latent semantic indexing (LSI) and the corresponding term-by-document matrix suggested by Berry and his co-authors. Instead of using deterministic methods to find the required number of first "k" singular triplets, we propose a stochastic approach. First, we use Monte Carlo method to sample and to build much smaller size term-by-document matrix (e.g. we build k x k matrix) from where we then find the first "k" triplets using standard deterministic methods. Second, we investigate how we can reduce the problem to finding the "k"-largest eigenvalues using parallel Monte Carlo methods. We apply these methods to the initial matrix and also to the reduced one. The algorithms are running on a cluster of workstations under MPI and results of the experiments arising in textual retrieval of Web documents as well as comparison of the stochastic methods proposed are presented. (C) 2003 IMACS. Published by Elsevier Science B.V. All rights reserved.

Sterically controlled recognition of macromolecular sequence information by molecular tweezers

Sequence-specific binding is demonstrated between pyrene-based tweezer molecules and soluble, high molar mass copolyimides. The binding involves complementary pi - pi stacking interactions, polymer chain-folding, and hydrogen bonding and is extremely sensitive to the steric environment around the pyromellitimide binding-site. A detailed picture of the intermolecular interactions involved has been obtained through single-crystal X-ray studies of tweezer complexes with model diimides. Ring-current magnetic shielding of polyimide protons by the pyrene '' arms '' of the tweezer molecule induces large complexation shifts of the corresponding H-1 NMR resonances, enabling specific triplet sequences to be identified by their complexation shifts. Extended comonomer sequences (triplets of triplets in which the monomer residues differ only by the presence or absence of a methyl group) can be '' read '' by a mechanism which involves multiple binding of tweezer molecules to adjacent diimide residues within the copolymer chain. The adjacent-binding model for sequence recognition has been validated by two conceptually different sets of tweezer binding experiments. One approach compares sequence-recognition events for copolyimides having either restricted or unrestricted triple-triplet sequences, and the other makes use of copolymers containing both strongly binding and completely nonbinding diimide residues. In all cases the nature and relative proportions of triple-triplet sequences predicted by the adjacent-binding model are fully consistent with the observed H-1 NMR data.

Vertical propagation of information in a middle atmosphere data assimilation system by gravity-wave drag feedbacks

The mesospheric response to the 2002 Antarctic Stratospheric Sudden Warming (SSW) is analysed using the Canadian Middle Atmosphere Model Data Assimilation System (CMAM-DAS), where it represents a vertical propagation of information from the observations into the data-free mesosphere. The CMAM-DAS simulates a cooling in the lowest part of the mesosphere which is accomplished by resolved motions, but which is extended to the mid- to upper mesosphere by the response of the model's non-orographic gravity-wave drag parameterization to the change in zonal winds. The basic mechanism is that elucidated by Holton consisting of a net eastward wave-drag anomaly in the mesosphere during the SSW, although in this case there is a net upwelling in the polar mesosphere. Since the zonal-mean mesospheric response is shown to be predictable, this demonstrates that variations in the mesospheric state can be slaved to the lower atmosphere through gravity-wave drag.

The information content of REIT credit rating actions and transparency

We examine the short-run and long-run price reaction of equity REIT shares following credit rating actions, testing the transparency of the REIT structure. Generally, the economic effect on the stock price is subdued for both upgrades and downgrades compared to prior literature examining the broader U.S. equity market. An examination of trading volume revealed a significant increase in trading in reaction to downgrade credit rating changes, with a more subdued response to upgrades. The findings support the notion that REITs are more publicly forthcoming about the expectation of positive news in comparison to negative news.

Information content and forecasting ability of sentiment indicators: case of real estate market

We evaluate a number of real estate sentiment indices to ascertain current and forward-looking information content that may be useful for forecasting demand and supply activities. Analyzing the dynamic relationships within a Vector Auto-Regression (VAR) framework and using the quarterly US data over 1988-2010, we test the efficacy of several sentiment measures by comparing them with other coincident economic indicators. Overall, our analysis suggests that the sentiment in real estate convey valuable information that can help predict changes in real estate returns. These findings have important implications for investment decisions, from consumers' as well as institutional investors' perspectives.

Information customization and food choice

In this paper we employ a hypothetical discrete choice experiment (DCE) to examine how much consumers are willing to pay to use technology to customize their food shopping. We conjecture that customized information provision can aid in the composition of a healthier shop. Our results reveal that consumers are prepared to pay relatively more for individual specic information as opposed to generic nutritional information that is typically provided on food labels. In arriving at these results we have examined various model specications including those that make use of ex-post de-brieng questions on attribute nonattendance and attribute ranking information and those that consider the time taken to complete the survey. Our main results are robust to the various model specications we examine

A variational approach to retrieve rain rate by combining information from rain gauges, radars, and microwave links

Accurate and reliable rain rate estimates are important for various hydrometeorological applications. Consequently, rain sensors of different types have been deployed in many regions. In this work, measurements from different instruments, namely, rain gauge, weather radar, and microwave link, are combined for the first time to estimate with greater accuracy the spatial distribution and intensity of rainfall. The objective is to retrieve the rain rate that is consistent with all these measurements while incorporating the uncertainty associated with the different sources of information. Assuming the problem is not strongly nonlinear, a variational approach is implemented and the Gauss–Newton method is used to minimize the cost function containing proper error estimates from all sensors. Furthermore, the method can be flexibly adapted to additional data sources. The proposed approach is tested using data from 14 rain gauges and 14 operational microwave links located in the Zürich area (Switzerland) to correct the prior rain rate provided by the operational radar rain product from the Swiss meteorological service (MeteoSwiss). A cross-validation approach demonstrates the improvement of rain rate estimates when assimilating rain gauge and microwave link information.

Persistence in diving American mink

Background American mink forage on land and in water, with aquatic prey often constituting a large proportion of their diet. Their long, thin body shape and relatively poor insulation make them vulnerable to heat loss, particularly in water, yet some individuals dive over 100 times a day. At the level of individual dives, previous research found no difference in dive depth or duration, or the total number of dives per day between seasons, but mink did appear to make more dives per active hour in winter than in summer. There was also no difference in the depth or duration of individual dives between the sexes, but there was some evidence that females made more dives per day than males. However, because individual mink dives tend to be extremely short in duration, persistence (quantified as the number of consecutive dives performed) may be a more appropriate metric with which to compare diving behaviour under different scenarios. Results Mink performed up to 28 consecutive dives, and dived continually for up to 36 min. Periods of more loosely aggregated diving (termed ‘aquatic activity sessions’) comprised up to 80 dives, carried out over up to 162.8 min. Contrary to our predictions, persistence was inversely proportional to body weight, with small animals more persistent than large ones, and (for females, but not for males) increased with decreasing temperature. For both sexes, persistence was greater during the day than during the night. Conclusions The observed body weight effect may point to inter-sexual niche partitioning, since in mink the smallest animals are females and the largest are males. The results may equally point to individual specialism’s, since persistence was also highly variable among individuals. Given the energetic costs involved, the extreme persistence of some animals observed in winter suggests that the costs of occasional prolonged activity in cold water are outweighed by the energetic gains. Analysing dive persistence can provide information on an animal’s physical capabilities for performing multiple dives and may reveal how such behaviour is affected by different conditions. Further development of monitoring and biologging methodology to allow quantification of hunting success, and thus the rewards obtained under alternative scenarios, would be insightful.

When enough is not enough: information overload and metacognitive decisions to stop studying information

People are often exposed to more information than they can actually remember. Despite this frequent form of information overload, little is known about how much information people choose to remember. Using a novel “stop” paradigm, the current research examined whether and how people choose to stop receiving new—possibly overwhelming—information with the intent to maximize memory performance. Participants were presented with a long list of items and were rewarded for the number of correctly remembered words in a following free recall test. Critically, participants in a stop condition were provided with the option to stop the presentation of the remaining words at any time during the list, whereas participants in a control condition were presented with all items. Across five experiments, we found that participants tended to stop the presentation of the items to maximize the number of recalled items, but this decision ironically led to decreased memory performance relative to the control group. This pattern was consistent even after controlling for possible confounding factors (e.g., task demands). The results indicated a general, false belief that we can remember a larger number of items if we restrict the quantity of learning materials. These findings suggest people have an incomplete understanding of how we remember excessive amounts of information.