Quantum field theory on a growing lattice

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth.Comment: 28 pages, 2 figures; v.2: added comments on defining energy, and reference

Songbird organotypic culture as an in vitro model for interrogating sparse sequencing networks

Sparse sequences of neuronal activity are fundamental features of neural circuit computation; however, the underlying homeostatic mechanisms remain poorly understood. To approach these questions, we have developed a method for cellular-resolution imaging in organotypic cultures of the adult zebra finch brain, including portions of the intact song circuit. These in vitro networks can survive for weeks, and display mature neuron morphologies. Neurons within the organotypic slices exhibit a diversity of spontaneous and pharmacologically induced activity that can be easily monitored using the genetically encoded calcium indicator GCaMP6. In this study, we primarily focus on the classic song sequence generator HVC and the surrounding areas. We describe proof of concept experiments including physiological, optical, and pharmacological manipulation of these exposed networks. This method may allow the cellular rules underlying sparse, stereotyped neural sequencing to be examined with new degrees of experimental control

On Linear Information Systems

Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information systems, providing a model of intuitionistic linear logic (a new-Seely category), with a "set-theoretic" interpretation of exponentials that recovers Scott continuous functions via the co-Kleisli construction. From a domain theoretic point of view, linear information systems are equivalent to prime algebraic Scott domains, which in turn generalize prime algebraic lattices, already known to provide a model of classical linear logic

Hierarchy Theory of Evolution and the Extended Evolutionary Synthesis: Some Epistemic Bridges, Some Conceptual Rifts

Contemporary evolutionary biology comprises a plural landscape of multiple co-existent conceptual frameworks and strenuous voices that disagree on the nature and scope of evolutionary theory. Since the mid-eighties, some of these conceptual frameworks have denounced the ontologies of the Modern Synthesis and of the updated Standard Theory of Evolution as unfinished or even flawed. In this paper, we analyze and compare two of those conceptual frameworks, namely Niles Eldredge’s Hierarchy Theory of Evolution (with its extended ontology of evolutionary entities) and the Extended Evolutionary Synthesis (with its proposal of an extended ontology of evolutionary processes), in an attempt to map some epistemic bridges (e.g. compatible views of causation; niche construction) and some conceptual rifts (e.g. extra-genetic inheritance; different perspectives on macroevolution; contrasting standpoints held in the “externalism–internalism” debate) that exist between them. This paper seeks to encourage theoretical, philosophical and historiographical discussions about pluralism or the possible unification of contemporary evolutionary biology

Causal categories: relativistically interacting processes

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a `causal category'. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

Evolutionary connectionism: algorithmic principles underlying the evolution of biological organisation in evo-devo, evo-eco and evolutionary transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions

Prediction of pathological stage in patients with prostate cancer: a neuro-fuzzy model

The prediction of cancer staging in prostate cancer is a process for estimating the likelihood that the cancer has spread before treatment is given to the patient. Although important for determining the most suitable treatment and optimal management strategy for patients, staging continues to present significant challenges to clinicians. Clinical test results such as the pre-treatment Prostate-Specific Antigen (PSA) level, the biopsy most common tumor pattern (Primary Gleason pattern) and the second most common tumor pattern (Secondary Gleason pattern) in tissue biopsies, and the clinical T stage can be used by clinicians to predict the pathological stage of cancer. However, not every patient will return abnormal results in all tests. This significantly influences the capacity to effectively predict the stage of prostate cancer. Herein we have developed a neuro-fuzzy computational intelligence model for classifying and predicting the likelihood of a patient having Organ-Confined Disease (OCD) or Extra-Prostatic Disease (ED) using a prostate cancer patient dataset obtained from The Cancer Genome Atlas (TCGA) Research Network. The system input consisted of the following variables: Primary and Secondary Gleason biopsy patterns, PSA levels, age at diagnosis, and clinical T stage. The performance of the neuro-fuzzy system was compared to other computational intelligence based approaches, namely the Artificial Neural Network, Fuzzy C-Means, Support Vector Machine, the Naive Bayes classifiers, and also the AJCC pTNM Staging Nomogram which is commonly used by clinicians. A comparison of the optimal Receiver Operating Characteristic (ROC) points that were identified using these approaches, revealed that the neuro-fuzzy system, at its optimal point, returns the largest Area Under the ROC Curve (AUC), with a low number of false positives (FPR = 0.274, TPR = 0.789, AUC = 0.812). The proposed approach is also an improvement over the AJCC pTNM Staging Nomogram (FPR = 0.032, TPR = 0.197, AUC = 0.582)