Stroke order normalization for improving recognition of online handwritten mathematical expressions

We present a technique based on stroke order normalization for improving recognition of online handwritten mathematical expressions (ME). The stroke order dependent system has less time complexity than the stroke order free system, but it must incorporate special grammar rules to cope with stroke order variations. The stroke order normalization technique solves this problem and also the problem of unexpected stroke order variations without increasing the time complexity of ME recognition. In order to normalize stroke order, the X-Y cut method is modified since its original form causes problems when structural components in ME overlap. First, vertically ordered strokes are located by detecting vertical symbols and their upper/lower components, which are treated as MEs and reordered recursively. Second, unordered strokes on the left side of the vertical symbols are reordered as horizontally ordered strokes. Third, the remaining strokes are reordered recursively. The horizontally ordered strokes are reordered from left to right, and the vertically ordered strokes are reordered from top to bottom. Finally, the proposed stroke order normalization is combined with the stroke order dependent ME recognition system. The evaluations on the CROHME 2014 database show that the ME recognition system incorporating the stroke order normalization outperforms all other systems that use only CROHME 2014 for training while the processing time is kept low

Augmented incremental recognition of online handwritten mathematical expressions

This paper presents an augmented incremental recognition method for online handwritten mathematical expressions (MEs). If an ME is recognized after all strokes are written (batch recognition), the waiting time increases significantly when the ME becomes longer. On the other hand, the pure incremental recognition method recognizes an ME whenever a new single stroke is input. It shortens the waiting time but degrades the recognition rate due to the limited context. Thus, we propose an augmented incremental recognition method that not only maintains the advantage of the two methods but also reduces their weaknesses. The proposed method has two main features: one is to process the latest stroke, and the other is to find the erroneous segmentations and recognitions in the recent strokes and correct them. In the first process, the segmentation and the recognition by Cocke-Younger-Kasami (CYK) algorithm are only executed for the latest stroke. In the second process, all the previous segmentations are updated if they are significantly changed after the latest stroke is input, and then, all the symbols related to the updated segmentations are updated with their recognition scores. These changes are reflected in the CYK table. In addition, the waiting time is further reduced by employing multi-thread processes. Experiments on our dataset and the CROHME datasets show the effectiveness of this augmented incremental recognition method, which not only maintains recognition rate even compared with the batch recognition method but also reduces the waiting time to a very small level

Chiral symmetry breaking in Hamiltonian QCD in Coulomb gauge

Spontaneous breaking of chiral symmetry is investigated in the Hamiltonian approach to QCD in Coulomb gauge. The quark wave functional is determined by the variational principle using an ansatz which goes beyond the commonly used BCS-type of wave functionals and includes the coupling of the quarks to the transversal spatial gluons. Using the lattice gluon propagator as input it is shown that the low energy chiral properties of the quarks, like the quark condensate and the constituent quark mass, are substantially increased by the coupling of the quarks to the spatial gluons. Our results compare favourably with the phenomenological values.Comment: 4 pages, 2 figure

Chiral perturbation theory, finite size effects and the three-dimensional XYXY model

We study finite size effects of the d=3 $XY$ model in terms of the chiral perturbation theory. We calculate by Monte Carlo simulations physical quantities which are, to order of $(1/L)^2$, uniquely determined only by two low energy constants. They are the magnetization and the helicity modulus (or the Goldstone boson decay constant) in infinite volume. We also pay a special attention to the region of the validity of the two possible expansions in the theory.Comment: 34 pages ( 9 PS files are included. harvmac and epsf macros are needed. ), KYUSHU-HET-17, SAGA-HE-6

Identification of the Changbaishan ‘Millennium’ (B-Tm) eruption deposit in the Lake Suigetsu (SG06) sedimentary archive, Japan: Synchronisation of hemispheric-wide palaeoclimate archives

The B-Tm tephra, dispersed during the highly explosive Changbaishan ‘Millennium’ eruption (ca. 940–950 CE) and a key marker layer within the Greenland ice cores, has now been identified in the Lake Suigetsu (SG06) sedimentary sequence, central Japan. The major element geochemistry of the volcanic glasses within this tephra layer are compared to a new glass dataset from the distal type-locality (Tomakomai Port, Hokkaido) and other published ‘Millennium’ eruption/B-Tm deposits, to verify this correlation. The discovery of the B-Tm tephra in the Lake Suigetsu record provides, to date, the most southerly identification of this ash and, crucially, the first direct tie-point between this high-resolution, mid-latitude palaeoclimate archive and the Greenland ice cores. These findings present significant encouragement for on-going research into the tephrostratigraphy of East Asia, focusing on the identification of widely-dispersed tephra layers which can facilitate the synchronisation of disparate palaeoclimate archives and thus enable the assessment of spatio-temporal variations in past climatic change