Full Triangle Research Articles

Counting Distinct Adjacent r-tuples in Words

For \(r=1,2,…, 6\), we obtain generating functions \(F^{(r)}_{k}(y)\) for words over the alphabet \([k]\), where \(y\) tracks the number of parts and \([y^n]\) is the total number of distinct adjacent \(r\)-tuples in words with \(n\) parts. In order to develop these generating functions for \(1\le r\le 3\), we make use of intuitive decompositions but for larger values of \(r\), we switch to the cluster analysis method for decorated texts that was introduced by Bassino et al. Finally, we account for the coefficients of these generating functions in terms of Stirling set numbers. This is done by putting forward the full triangle of coefficients for all the sub-cases where \(r=5\) and 6. This latter is shown to depend on both periodicity and number of letters used in the \(r\)-tuples.

Prefixes of Stanley’s Catalan Paths with Odd Returns to the \(x\)-axis–Standard Version and Skew Catalan-Stanley Paths

For \(r=1,2,…, 6\), we obtain generating functions \(F^{(r)}_{k}(y)\) for words over the alphabet \([k]\), where \(y\) tracks the number of parts and \([y^n]\) is the total number of distinct adjacent \(r\)-tuples in words with \(n\) parts. In order to develop these generating functions for \(1\le r\le 3\), we make use of intuitive decompositions but for larger values of \(r\), we switch to the cluster analysis method for decorated texts that was introduced by Bassino et al. Finally, we account for the coefficients of these generating functions in terms of Stirling set numbers. This is done by putting forward the full triangle of coefficients for all the sub-cases where \(r=5\) and 6. This latter is shown to depend on both periodicity and number of letters used in the \(r\)-tuples.

Classifying edge-biregular maps of negative prime Euler characteristic

An edge-biregular map arises as a smooth normal quotient of a unique index-two subgroup of a full triangle group acting with two edge-orbits. We give a classification of all finite edge-biregular maps on surfaces of negative prime Euler characteristic.

Triangular Regions Representations for Matching Images With Viewpoint Changes

This paper proposes triangular region representations based on keypoints detected in images with viewpoint changes. The strongest keypoints in the reference and query images are allocated individually using a previously published contourlet-based approach to determine the keypoints. These selected keypoints serve as vertices of the triangular regions to be transformed into rectangular representations as simple numeric matrices. The suggested representation methods used to form rectangular matrices are full triangle representation (FTR) and a lighter representation called triangle medians and sides representation (TMSR). For the former, the intensity values along the lines connecting the anchor keypoint to the points between the other two triangular vertices form the rows of the representation matrix. These two triangle vertices are located in an allotted window around the anchor keypoint from the nearby keypoints. For the latter, the intensity values on the six triangular lines, medians, and sides formed the resulting rectangular matrix. The proposed representations are validated for image-matching applications using a descriptor-less matching method. Moreover, the performances of these algorithms are compared with those of traditional algorithms. The results confirmed the superiority of the proposed method over these algorithms.

Introducing edge-biregular maps

We introduce the concept of alternate-edge-colourings for maps and study highly symmetric examples of such maps. Edge-biregular maps of type (k, l) occur as smooth normal quotients of a particular index two subgroup of T_{k,l}, the full triangle group describing regular plane (k, l)-tessellations. The resulting colour-preserving automorphism groups can be generated by four involutions. We explore special cases when the usual four generators are not distinct involutions, with constructions relating these maps to fully regular maps. We classify edge-biregular maps when the supporting surface has non-negative Euler characteristic, and edge-biregular maps on arbitrary surfaces when the colour-preserving automorphism group is isomorphic to a dihedral group.

A Smartphone App (TRIANGLE) to Change Cardiometabolic Risk Behaviors in Women Following Gestational Diabetes Mellitus: Intervention Mapping Approach

BackgroundGestational diabetes mellitus (GDM) is the most common complication during pregnancy and is associated with an increased risk for the development of cardiometabolic diseases. Behavioral interventions can reduce this risk, but current solutions insufficiently address the requirements for such a program. The systematic development of a scalable mobile health (mHealth) promotion program for mothers during the first years post-GDM may contribute to solving this problem.ObjectiveThe aim of this project was to systematically plan and develop a theory- and evidence-based mHealth intervention to change cardiometabolic risk behaviors in women during the first 5 years post-GDM that meets women’s expected standards of commercial health apps.MethodsThe intervention mapping steps 1 to 4 structured the systematic planning and development of the mHealth program described in this paper. Steps 1 and 2 led to a theory- and evidence-based logic model of change for cardiometabolic health. Based on this model, the prevention program was designed (step 3) and produced (step 4) in cooperation with industrial partners to ensure a high technological standard of the resulting smartphone app for the iPhone (Apple Inc). Step 4 included a user study with women during the first 5 years post-GDM once a beta version of the app (“TRIANGLE”) was available. The user study comprised 2 test rounds of 1 week (n=5) and 4 weeks (n=6), respectively. The tests included validated questionnaires on user acceptance, user logs, and think-alouds with semistructured interviews.ResultsThe novel TRIANGLE app is among the first self-paced smartphone apps for individual habit change in the 3 lifestyle areas of physical activity, nutrition, and psychosocial well-being. The 3 core features—a challenge system, human coaching, and a library—address 11 behavioral determinants with 39 behavior change methods to support lifestyle changes. Participants in the user study showed a high acceptance, high perceived quality, and high perceived impact of the TRIANGLE app on their health behaviors. Participants tested the app regularly, used it intuitively, and suggested improvements. We then adapted the TRIANGLE app according to the insights from the user study before the full TRIANGLE program production.ConclusionsThe intervention mapping approach was feasible to plan and develop an innovative and scalable smartphone solution for women during the first 5 years post-GDM. The resulting TRIANGLE intervention has the potential to support behavior change for cardiometabolic disease prevention. However, the app needs further refinement and testing in clinical trials. Intervention mapping steps 5 (implementation plan) and 6 (evaluation plan) may support the integration of the TRIANGLE intervention into routine care.Trial RegistrationGerman Clinical Trials Register DRKS00012736; https://www.drks.de/DRKS00012736

Does the PMSP connectionist model of single word reading learn to read in the same way as a child?

The Plaut, McClelland, Seidenberg and Patterson (1996) connectionist model of reading was evaluated at two points early in its training against reading data collected from British children on two occasions during their first year of literacy instruction. First, the network's non‐word reading was poor relative to word reading when compared with the children. Second, the network made more non‐lexical than lexical errors, the opposite pattern to the children. Three adaptations were made to the training of the network to bring it closer to the learning environment of a child: an incremental training regime was adopted; the network was trained on grapheme–phoneme correspondences; and a training corpus based on words found in children's early reading materials was used. The modifications caused a sharp improvement in non‐word reading, relative to word reading, resulting in a near perfect match to the children's data on this measure. The modified network, however, continued to make predominantly non‐lexical errors, although evidence from a small‐scale implementation of the full triangle framework suggests that this limitation stems from the lack of a semantic pathway. Taken together, these results suggest that, when properly trained, connectionist models of word reading can offer insights into key aspects of reading development in children.

An Information Approach to International Currencies

This paper addresses currency competition from an information perspective. Transactions in traditional models do not convey information, so transaction costs - the driver of competition outcomes - are driven by market size. In our model, transactions do convey information (consistent with recent empirical findings). Several important departures arise. First, adding the information dimension resolves the traditional indeterminacy of currency trade patterns (by mitigating the concentrating force of market-size economies). Second, whether transactions are executed directly or through a vehicle actually affects prices (because these trading methods do not in general reveal the same information). Third, our model provides a new rationale for why some currency pairs never trade directly (information is not sufficiently symmetric to support trading). Fourth, our model formalizes the arbitrage process and shows that arbitrage transaction quantities and price levels are jointly determined. Empirically, the paper provides a first integrated analysis of transactions in a triangle of markets: Yen/$, $/Euro, and Yen/Euro. Data for the full triangle permits comparison of direct, indirect and arbitrage transactions, for each pair. The information model makes the important prediction that transactions should affect prices across markets (e.g., flow in the Yen/$ market should convey information relevant to $/Euro and Yen/Euro prices), which is borne out.

Saccadic localization of occluded targets

Saccadic eye movements are able to localize spatially-extended targets, including patterns of random dots and simple shapes, with a high degree of precision [McGowan, Kowler, Sharma & Chubb (1998). Vision Research, 38, 895–909; Melcher & Kowler (1999). Vision Research, 39, 2929–2946]. This paper investigates the representations of object shape that guide saccades. We studied saccadic localization of partially-occluded triangles (two or three vertices removed) to find out whether saccades have access to a representation of the full shape, despite the missing portions. Targets were configured so that they could be seen either as triangles, which were partially occluded by polygons, or as fragments in front of the same polygons. Subjects tried to saccade to the inferred full triangle and a discrimination paradigm was used to evaluate their success. Occlusion cues were ineffective in that saccades directed to the occluded triangles landed near the center of the visible fragment, even when it was configured as a triangle behind occluders. Removing the occluders and leaving only three segments of the triangle (vertices removed) helped somewhat, but performance never resembled that achieved with either a full triangle or a 3-dot configuration. We conclude that the saccadic system is insensitive to at least some cues that can be used to infer the shape of objects. For occluded targets, the representation used by saccades may be closer to the configuration of the retinal image.

Exact and approximate triangle amplitudes for (in-)elastic three-body processes with charged particles

The triangle amplitudes, which within the framework of the multiple-scattering approach represent the leading contribution to the amplitude for three-body elastic and inelastic reactions, contain the off-shell Coulomb T-matrix describing the intermediate-state scattering of the projectile off each of the target particles. We present results of the exact numerical calculation of that amplitude in which the rescattering particles have charges of opposite sign (`attractive case'), for several atomic processes. This is facilitated by a `new' representation of the Coulomb T-matrix which turns out to be very effective for numerical purposes. One interesting result is that the charge sensitivity of the full triangle amplitude apparently disappears at the elastic threshold, for all scattering angles. Furthermore, we propose a new approximation for the triangle amplitudes which can be viewed as a `renormalization' by a simple analytic expression, of the well known approximation which consists in replacing by the potential . While the latter is known to be generally inadequate, this new approximation is shown to yield results in excellent agreement with the numerically calculated exact amplitude, for atomic elastic reactions, over a wide range of (medium to high) projectile energies and scattering angles (including the near-forward-scattering direction). An even simpler approximate amplitude is derived which contains no quadratures at all. It yields similarly good results provided the masses of the two particles experiencing intermediate-state rescattering are of the same order of magnitude but differ from that of the spectator particle. In addition, the explicit forms of the approximate amplitudes are used to derive a variety of interesting theoretical results.

Dietary treatment of hyperlipidemias by using a food exchange table method. A preliminary report.

To overcome the difficulties in the dietary treatment of hyperlipidemias, the method of food exchange table for hyperlipidemia has been developed, in which each food of 80 calories was handled as one unit and the cholesterol and fatty acid content in one unit of food were shown as number of black circle(s) and triangle(s). Each full black circle indicated 50 mg of food cholesterol, and a full triangle meant that S-1/2P value of food was 0.5. The patients were instructed to take daily diet containing not more than 5 black circles or +4 trangles in the total. Serum cholesterol and triglycerides of the patients thus instructed were compared with those of patients on ordinary dietary regimens. Although this method still failed to effect statisfactory reduction in serum lipid concentrations, the method made it easier for a dietician to explain the dietary regimen and also for a patient to observe dietary treatment. For further improvement, more strict exchange rules for varieties of food had to be established without causing imbalance in the nutritional ingredients of dietary regimens.