Undecidability of Multiplicative Subexponential Logic

Subexponential logic is a variant of linear logic with a family of exponential connectives--called subexponentials--that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that classical propositional multiplicative linear logic extended with one unrestricted and two incomparable linear subexponentials can encode the halting problem for two register Minsky machines, and is hence undecidable.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441

How Much Information is in a Jet?

Machine learning techniques are increasingly being applied toward data analyses at the Large Hadron Collider, especially with applications for discrimination of jets with different originating particles. Previous studies of the power of machine learning to jet physics has typically employed image recognition, natural language processing, or other algorithms that have been extensively developed in computer science. While these studies have demonstrated impressive discrimination power, often exceeding that of widely-used observables, they have been formulated in a non-constructive manner and it is not clear what additional information the machines are learning. In this paper, we study machine learning for jet physics constructively, expressing all of the information in a jet onto sets of observables that completely and minimally span N-body phase space. For concreteness, we study the application of machine learning for discrimination of boosted, hadronic decays of Z bosons from jets initiated by QCD processes. Our results demonstrate that the information in a jet that is useful for discrimination power of QCD jets from Z bosons is saturated by only considering observables that are sensitive to 4-body (8 dimensional) phase space.Comment: 14 pages + appendices, 10 figures; v2: JHEP version, updated neural network, included deeper network and boosted decision tree result

Anthropogenic Harvesting Pressure and Changes in Life History: Insights from a Rocky Intertidal Limpet

The importance of large breeding individuals for maintaining the health of marine fish and invertebrate populations has long been recognized. Unfortunately, decades of human harvesting that preferentially remove larger individuals have led to drastic reductions in body sizes of many of these species. Such size-selective harvesting is particularly worrisome for sequentially hermaphroditic species where the larger size classes are composed primarily of one sex. Whether these species can maintain stable sex ratios under sustained harvesting pressure depends on the level of plasticity of their life-history traits. Here, we show that populations of a marine limpet (Lottia gigantea) can adjust a fundamental aspect of their life history (the timing of sex change) when subjected to size-selective harvesting. As predicted by theoretical models, individuals from harvested populations change sex at smaller sizes and grow at slower rates compared to individuals from protected populations. In addition, the relative size at which the change from male to female occurs remains constant (?0.75; size at sex change/maximum size) across populations, regardless of harvesting pressure. Our results show that population-level demographic and life-history data, in conjunction with existing theory, can be sufficient to predict the responses of sequential hermaphrodites to harvesting pressure. Furthermore, they suggest such species can potentially adapt to size-selective harvesting

Automating the Construction of Jet Observables with Machine Learning

Machine-learning assisted jet substructure tagging techniques have the potential to significantly improve searches for new particles and Standard Model measurements in hadronic final states. Techniques with simple analytic forms are particularly useful for establishing robustness and gaining physical insight. We introduce a procedure to automate the construction of a large class of observables that are chosen to completely specify $M$-body phase space. The procedure is validated on the task of distinguishing $H\rightarrow b\bar{b}$ from $g\rightarrow b\bar{b}$, where $M=3$ and previous brute-force approaches to construct an optimal product observable for the $M$-body phase space have established the baseline performance. We then use the new method to design tailored observables for the boosted $Z'$ search, where $M=4$ and brute-force methods are intractable. The new classifiers outperform standard $2$-prong tagging observables, illustrating the power of the new optimization method for improving searches and measurement at the LHC and beyond.Comment: 15 pages, 8 tables, 12 figure

A Hybrid Linear Logic for Constrained Transition Systems

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus