Graded Betti numbers of powers of ideals

Using the concept of vector partition functions, we investigate the asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field. Our main results state that if the polynomial ring is equipped with a positive \ZZ-grading, then the Betti numbers of powers of ideals are encoded by finitely many polynomials. More precisely, in the case of \ZZ-grading, \ZZ^2 can be splitted into a finite number of regions such that each region corresponds to a polynomial that depending to the degree $(\mu, t)$, \dim_k \left(\tor_i^S(I^t, k)_{\mu} \right) is equal to one of these polynomials in $(\mu, t)$. This refines, in a graded situation, the result of Kodiyalam on Betti numbers of powers of ideals. Our main statement treats the case of a power products of homogeneous ideals in a \ZZ^d-graded algebra, for a positive grading.Comment: 20 page

Interacting Spinors-Scalars and AdS/CFT Correspondence

By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.Comment: The crucial role of the surface term in the action to generate the correlation functions quadratic in spinors is considered. LaTeX file, 8 page

Results of the WMT17 metrics shared task

This paper presents the results of the WMT17 Metrics Shared Task. We asked participants of this task to score the outputs of the MT systems involved in the WMT17 news translation task and Neural MT training task. We collected scores of 14 metrics from 8 research groups. In addition to that, we computed scores of 7 standard metrics (BLEU, SentBLEU, NIST, WER, PER, TER and CDER) as baselines. The collected scores were evaluated in terms of system-level correlation (how well each metric’s scores correlate with WMT17 official manual ranking of systems) and in terms of segment level correlation (how often a metric agrees with humans in judging the quality of a particular sentence). This year, we build upon two types of manual judgements: direct assessment (DA) and HUME manual semantic judgements

Results of the WMT15 Tuning Shared Task

This paper presents the results of the WMT15 Tuning Shared Task. We provided the participants of this task with a complete machine translation system and asked them to tune its internal parameters (feature weights). The tuned systems were used to translate the test set and the outputs were manually ranked for translation quality. We received 4 submissions in the English-Czech and 6 in the Czech-English translation direction. In addition, we ran 3 baseline setups, tuning the parameters with standard optimizers for BLEU score