Solving Tree Problems with Category Theory

Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability to solve wide ranges of problems. This situation begs the question of the existence of principles that underlie general problem-solving capabilities. We approach this question through the mathematical formulation of analogies across different problems and solutions. We focus in particular on problems that could be represented as tree-like structures. Most importantly, we adopt a category-theoretic approach in formalising tree problems as categories, and in proving the existence of equivalences across apparently unrelated problem domains. We prove the existence of a functor between the category of tree problems and the category of solutions. We also provide a weaker version of the functor by quantifying equivalences of problem categories using a metric on tree problems.Comment: 10 pages, 4 figures, International Conference on Artificial General Intelligence (AGI) 201

Estimands: bringing clarity and focus to research questions in clinical trials

Precise specification of the research question and associated treatment effect of interest is essential in clinical research, yet recent work shows that they are often incompletely specified. The ICH E9 (R1) Addendum on Estimands and Sensitivity Analysis in Clinical Trials introduces a framework that supports researchers in precisely and transparently specifying the treatment effect they aim to estimate in their clinical trial. In this paper, we present practical examples to demonstrate to all researchers involved in clinical trials how estimands can help them to specify the research question, lead to a better understanding of the treatment effect to be estimated and hence increase the probability of success of the trial

One- and two-photon activated phototoxicity of conjugated porphyrin dimers with high two-photon absorption cross sections

Two-photon excited photodynamic therapy (PDT) has the potential to provide a highly targeted treatment for neoplastic diseases, as excitation can be pin-pointed to small volumes at the laser focus. In addition, two-photon PDT offers deeper penetration into mammalian tissue due to the longer wavelength of irradiation. Here we report the one-photon and two-photon excited PDT results for a collection of conjugated porphyrin dimers with high two-photon absorption cross sections. These dimers demonstrate high one-photon PDT efficacy against a human ovarian adenocarcinoma cell line (SK-OV-3) and exhibit no significant dark-toxicity at concentrations of up to 20 microM. Their one-photon excited PDT efficiencies, following irradiation at 657 nm, approach that of Visudyne, a drug used clinically for PDT. We investigated and optimised the effect of the photosensitizer concentration, incubation time and the light dose on the PDT efficacy of these dimers. These studies led to the selection of P2C2-NMeI as the most effective porphyrin dimer. We have demonstrated that P2C2-NMeI undergoes a two-photon activated process following excitation at 920 nm (3.6-6.8 mW, 300 fs, 90 MHz) and compared it to Visudyne. We conclude that the in vitro two-photon PDT efficacy of P2C2-NMeI is about twice that of Visudyne. This result highlights the potential of this series of porphyrin dimers for two-photon PDT

Developing a Business Case for the Care Coordination and Transition Management Model: Need, Metrics, and Measures

In this descriptive qualitative study, nurse and healthcare leaders\u27 experiences, perceptions of care coordination and transition management (CCTM®), and insights as to how to foster adoption of the CCTM RN role in nursing education, practice across the continuum, and policy were explored. Twenty-five barriers to recognition and adoption of CCTM RN practice across the continuum were identified and categorized. Implications of these findings, recommendations for adoption of CCTM RN practice across the care continuum, and strategies for reimbursement policies are discussed

Making hard choices easier: a prospective, multicentre study to assess the efficacy of a fertility-related decision aid in young women with early-stage breast cancer

BACKGROUND: Fertility is a priority for many young women with breast cancer. Women need to be informed about interventions to retain fertility before chemotherapy so as to make good quality decisions. This study aimed to prospectively evaluate the efficacy of a fertility-related decision aid (DA). METHODS: A total of 120 newly diagnosed early-stage breast cancer patients from 19 Australian oncology clinics, aged 18–40 years and desired future fertility, were assessed on decisional conflict, knowledge, decision regret, and satisfaction about fertility-related treatment decisions. These were measured at baseline, 1 and 12 months, and were examined using linear mixed effects models. RESULTS: Compared with usual care, women who received the DA had reduced decisional conflict (β=−1.51; 95%CI: −2.54 to 0.48; P=0.004) and improved knowledge (β=0.09; 95%CI: 0.01–0.16; P=0.02), after adjusting for education, desire for children and baseline uncertainty. The DA was associated with reduced decisional regret at 1 year (β=−3.73; 95%CI: −7.12 to −0.35; P=0.031), after adjusting for education. Women who received the DA were more satisfied with the information received on the impact of cancer treatment on fertility (P<0.001), fertility options (P=0.005), and rated it more helpful (P=0.002), than those who received standard care. CONCLUSION: These findings support widespread use of this DA shortly after diagnosis (before chemotherapy) among younger breast cancer patients who have not completed their families

Importance of tropical tuna for seabird foraging over a marine productivity gradient

Foraging with tuna is a well-documented seabird strategy, referred to as facilitated foraging. However, despite this behaviour being considered almost obligatory in nutrient-poor tropical waters, little data exist on its relative importance to individual colonies. Therefore, to examine facilitated foraging under different patterns of nutrient availability, we tracked wedgetailed shearwaters Ardenna pacifica from 2 colonies, one tropical and one subtropical, situated in waters of contrasting productivity. Shearwater foraging behaviour was assessed relative to oceanographic covariates and predicted distributions for multiple tropical tuna species and ageclasses, simulated by an existing ecosystem model (SEAPODYM). Shearwaters from both colonies undertook long trips to deep, pelagic waters close to seamounts and foraged most often at fronts and eddies. Micronektonic and adult tuna age classes were highly correlated in space. Predation between these tuna age classes represents a likely source of facilitated foraging opportunities for shearwaters. At broad spatio-temporal scales, shearwaters consistently foraged in areas with higher predicted adult skipjack and micronektonic tuna densities and avoided adult bigeye tuna. At finer spatio-temporal scales, dynamic ocean features aggregated tuna of all sizes. Enhanced tuna density at these locations increased the likelihood of shearwater foraging activity. Long trips in the tropics targeted oligotrophic waters with higher tuna densities. Long trips in the subtropics targeted enhanced productivity, but in some years shifted to target the same oligotrophic, tunadense waters used by tropical conspecifics. We conclude that facilitated foraging with tuna is consistently important to the tropical breeding population and becomes increasingly important to the subtropical population in years of low marine productivity

Experimental Analysis of Nonlinear Impairments in Fibre Optic Transmission Systems up to 7.3 THz

An effective way of increasing the overall optical fibre capacity is by expanding the bandwidth used to transmit signals. In this paper, the impact of expanding the transmission bandwidth on the optical communication system is experimentally studied using the achievable rates as a performance metric. The trade-offs between the use of larger bandwidths and higher nonlinear interference (NLI) noise is experimentally and theoretically analysed. The growth of NLI noise is investigated for spectral bandwidths from 40 GHz up to 7.3 THz using 64-QAM and Nyquist pulse-shaping. Experimental results are shown to be in line with the predictions from the Gaussian-Noise model showing a logarithmic growth in NLI noise as the signal bandwidth is extended. A reduction of the information rate of only 10 % was found between linear and non-linear transmission across several transmission bandwidths, increasing up to 7.3 THz. Finally, the power transfer between channels due to stimulated Raman scattering effect is analysed showing up to 2 dB power tilt at optimum power for the largest transmitted bandwidth of 7.3 THz

Categorial Compositionality III: F-(co)algebras and the Systematicity of Recursive Capacities in Human Cognition

Human cognitive capacity includes recursively definable concepts, which are prevalent in domains involving lists, numbers, and languages. Cognitive science currently lacks a satisfactory explanation for the systematic nature of such capacities (i.e., why the capacity for some recursive cognitive abilities–e.g., finding the smallest number in a list–implies the capacity for certain others–finding the largest number, given knowledge of number order). The category-theoretic constructs of initial F-algebra, catamorphism, and their duals, final coalgebra and anamorphism provide a formal, systematic treatment of recursion in computer science. Here, we use this formalism to explain the systematicity of recursive cognitive capacities without ad hoc assumptions (i.e., to the same explanatory standard used in our account of systematicity for non-recursive capacities). The presence of an initial algebra/final coalgebra explains systematicity because all recursive cognitive capacities, in the domain of interest, factor through (are composed of) the same component process. Moreover, this factorization is unique, hence no further (ad hoc) assumptions are required to establish the intrinsic connection between members of a group of systematically-related capacities. This formulation also provides a new perspective on the relationship between recursive cognitive capacities. In particular, the link between number and language does not depend on recursion, as such, but on the underlying functor on which the group of recursive capacities is based. Thus, many species (and infants) can employ recursive processes without having a full-blown capacity for number and language

Categorial Compositionality: A Category Theory Explanation for the Systematicity of Human Cognition

Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with the data, both nonetheless fail to fully explain it. Category theory, a branch of mathematics, provides an alternative explanation based on the formal concept of adjunction, which relates a pair of structure-preserving maps, called functors. A functor generalizes the notion of a map between representational states to include a map between state transformations (or processes). In a formal sense, systematicity is a necessary consequence of a higher-order theory of cognitive architecture, in contrast to the first-order theories derived from Classicism or Connectionism. Category theory offers a re-conceptualization for cognitive science, analogous to the one that Copernicus provided for astronomy, where representational states are no longer the center of the cognitive universe—replaced by the relationships between the maps that transform them