A categorical framework for the quantum harmonic oscillator

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Surprisingly, generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures.Comment: 44 pages, many figure

Multifocal Renal Cell Carcinoma: Clinicopathologic Features and Outcomes for Tumors ≤4 cm

A significant increase in the incidental detection of small renal tumors has been observed with the routine use of cross-sectional abdominal imaging. However, the proportion of small renal tumors associated with multifocal RCC has yet to be established. Here then, we report our experience with the treatment of multifocal RCC in which the primary tumor was ≤4 cm. In our series of 1113 RCC patients, 5.4% (60/1113) had multifocal disease at the time of nephrectomy. Discordant histology was present in 17% (10/60) of patients with multifocal RCC. Nephron sparing surgery was utilized more frequently in patients with solitary tumors. Overall, cancer-specific, and distant metastasis-free survival appeared to be similar between multifocal and solitary tumors. These findings are consistent with previous series which evaluated multifocal RCC with tumors >4 cm. With the known incidence of multifocality RCC, careful inspection of the entire renal unit should be performed when performing nephron sparing surgery

Editors' Review and Introduction:The Cultural Evolution of Cognition

This topic addresses a question of key interest to cognitive science, namely which factors may have triggered, constrained, or shaped the course of cognitive evolution. It highlights the relevance of culture as a driving force in this process, with a special focus on social learning and language, conceptual tools, and material culture. In so doing, the topic combines two goals: to provide an overview of current empirical and theoretical work leading this field, tailored for a wider cognitive science audience, and to investigate the potential for integrating multiple perspectives across several timescales and levels of analysis, from the microlevel of individual behavior to the macrolevel of cultural change and language diversification. One key purpose is to assess the extent to which the different research approaches can cross‐fertilize each other, thereby also contributing to the advancement of cognitive science more broadly.acceptedVersio

Evolution in Quantum Causal Histories

We provide a precise definition and analysis of quantum causal histories (QCH). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. We show that this local description of evolution is sufficient and that unitary evolution can be recovered wherever it should actually be expected. This formalism may describe a quantum cosmology without an assumption of global hyperbolicity; it is thus more general than the Wheeler-DeWitt approach. The structure of a QCH is also closely related to quantum information theory and algebraic quantum field theory on a causal set.Comment: 20 pages. 8 figures. (v3: minor corrections, additional references [2,3]) to appear in CQ

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

Renal angiomyolipoma presenting with massive retroperitoneal haemorrhage due to deranged clotting factors: a case report

BACKGROUND: Angiomyolipomata of the kidney are unusual lesions composed of abnormal vasculature, smooth muscle, and adipose elements. They may be associated with tuberous sclerosis and occasionally present with flank pain, a palpable mass, and gross haematuria. As angiomyolipomata grow their risk of bleeding increases, with a greater than 50% chance of significant bleeding in lesions > 4 cm; anticoagulant therapy accentuates this risk. CASE PRESENTATION: A case of massive retroperitoneal haemorrhage in a patient on warfarin is presented. The underlying diagnosis of renal angiomyolipoma was diagnosed based on CT findings. Emergency resuscitation and selective interpolar arterial embolization was performed which saved the patient's life as well as his kidney. CONCLUSION: This case illustrates the clinical scenario of massive retroperitoneal haemorrhage in an anticoagulated patient with renal angiomyolipomata. In the emergent situation, adequate resuscitation along ABC principles, as well as control of haemorrhage with either nephrectomy (partial or radical), non-selective renal arterial embolization, or selective embolization of the feeding vessel(s), is necessary. For this to occur, it is imperative to consider the diagnosis early in warfarinized patients (and others at risk of bleeding) who present with abdominal pain. The authors hope this case report highlights to readers the clinical scenario of massive retroperitoneal haemorrhage in anticoagulated patients with renal angiomyolipomata so that they can deal appropriately with such presentations

Quantum Speedup and Categorical Distributivity

This paper studies one of the best known quantum algorithms - Shor's factorisation algorithm - via categorical distributivity. A key aim of the paper is to provide a minimal set of categorical requirements for key parts of the algorithm, in order to establish the most general setting in which the required operations may be performed efficiently. We demonstrate that Laplaza's theory of coherence for distributivity provides a purely categorical proof of the operational equivalence of two quantum circuits, with the notable property that one is exponentially more efficient than the other. This equivalence also exists in a wide range of categories. When applied to the category of finite dimensional Hilbert spaces, we recover the usual efficient implementation of the quantum oracles at the heart of both Shor's algorithm and quantum period-finding generally; however, it is also applicable in a much wider range of settings.Comment: 17 pages, 11 Figure

Simulating causal collapse models

We present simulations of causal dynamical collapse models of field theories on a 1+1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalising the fundamental field can overcome its noisiness and argue that this coarse grained renormalised field will show interesting structure if the state vector does on the coarse grained scale.Comment: 18 pages, 8 fugures, LaTeX, Reference added, discussion of probability distribution of labellings correcte

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