Stable Asymptotically Free Extensions (SAFEs) of the Standard Model

We consider possible extensions of the standard model that are not only completely asymptotically free, but are such that the UV fixed point is completely UV attractive. All couplings flow towards a set of fixed ratios in the UV. Motivated by low scale unification, semi-simple gauge groups with elementary scalars in various representations are explored. The simplest model is a version of the Pati-Salam model. The Higgs boson is truly elementary but dynamical symmetry breaking from strong interactions may be needed at the unification scale. A hierarchy problem, much reduced from grand unified theories, is still in need of a solution.Comment: 26 pages. Published version, typos correcte

Sequential Pattern Mining with Multidimensional Interval Items

In real sequence pattern mining scenarios, the interval information between two item sets is very important. However, although existing algorithms can effectively mine frequent subsequence sets, the interval information is ignored. This paper aims to mine sequential patterns with multidimensional interval items in sequence databases. In order to address this problem, this paper defines and specifies the interval event problem in the sequential pattern mining task. Then, the interval event items framework is proposed to handle the multidimensional interval event items. Moreover, the MII-Prefixspan algorithm is introduced for the sequential pattern with multidimensional interval event items mining tasks. This algorithm adds the processing of interval event items in the mining process. We can get richer and more in line with actual needs information from mined sequence patterns through these methods. This scheme is applied to the actual website behaviour analysis task to obtain more valuable information for web optimization and provide more valuable sequence pattern information for practical problems. This work also opens a new pathway toward more efficient sequential pattern mining tasks

Every ambiguity isn’t syntactic in nature: Testing the Rational Speech Act model of scope ambiguity

Utterances like ‘Every guest didn’t leave’ are ambiguous between a reading according to which no guest left and a reading according to which not all of the guests left. This ambiguity is often explained by assuming that ‘every-not’ utterances have two different syntactic parses. However, experimental studies have shown that pragmatic factors, such as prior probabilities and the question under discussion, also play an important role in the interpretation of ambiguous ‘every-not’ utterances. Recently, Scontras and Pearl (2020) put forward a probabilistic model of ambiguity resolution that makes it possible to quantify the relative contribution of syntactic and pragmatic factors. Here, we present three experiments aimed at testing this model and measuring the division of labor between syntax and pragmatics. Our results suggest that variability in the interpretation of ‘every-not’ utterances can be explained almost entirely in terms of pragmatics, suggesting only a marginal role for syntax

Sums of Evenly Spaced Binomial Coefficients

We provide a combinatorial proof of a formula for the sum of evenly spaced binomial coefficients. This identity, along with a generalization, are proved by counting weighted walks on a graph