A common issue in the study of Turing machines (TMs) is the halting problem, or whether and when a TM will cease moving. Generally, this problem has been proved to be uncomputable, though it is possible to determine halting probabilities for more specific cases. In the following study, halting probabilities were determined using two unconventional definitions of halting. The first defines halting as the point where a machine reaches a certain, prespecified step; the second defines halting as the point where cell states stop changing (though head states may still differ from step to step). Due to computational limitations, the halting probabilities for TMs with fewer head and cell states have been more thoroughly studied than for more complicated machines, but nonetheless some data has been garnered concerning those. The TMs studied ranged from two possible head states and two possible cell states to six possible head states and six possible cell states.

Decays of Higgs boson-like particles into multileptons is a well-motivated process for investigating physics beyond the Standard Model (SM). A unique feature of this final state is the precision with which the SM is known. As a result, simulations are used directly to estimate the background. Current searches consider specific models and typically focus on those with a single free parameter to simplify the analysis and interpretation. In this paper, we explore recent proposals for signal model agnostic searches using machine learning in the multilepton final state. These tools can be used to simultaneously search for many models, some of which have no dedicated search at the Large Hadron Collider. We find that the machine learning methods offer broad coverage across parameter space beyond where current searches are sensitive, with a necessary loss of performance compared to dedicated searches by only about one order of magnitude.

Obs erving the clus tering of galaxies allows us to calculate cos mological parameters neces s ary for unders tanding dark energy. However, as the dens ity of obs erved objects increas es , the probability of thes e objects blending likewis e increas es , caus ing multiple galaxies to be obs erved as one. This affects the calculated values of parameters s uch as the galaxy bias (b) and the matter energy dens ity (Ω M ). To s ee whether the bias from incorrectly inferring the galaxy count is s ignificant, we compare the correlation functions in s imulated data for "obs erved" and "true" data s ets with one-to-one and multiple-to-one corres pondences .

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