Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ring $R[x,f]$ that are Artinian as $R$-modules and the category of right $R[x,f]$-modules that are Noetherian as $R$-modules.Comment: 16 pages, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society. This revised version includes two additionl references and points out that some of the results have been obtained independently by M. Blickle and G. Boeckl

Large Abdominal Wall Endometrioma Following Laparoscopic Hysterectomy

Although extrapelvic endometriosis is rare, it should be considered in the diagnosis of the female patient with an abdominal mass and pain who has had a previous surgical procedure

Constructing Fluorogenic Bacillus Spores (F-Spores) via Hydrophobic Decoration of Coat Proteins

Background: Bacterial spores are protected by a coat consisting of about 60 different proteins assembled as a biochemically complex structure with intriguing morphological and mechanical properties. Historically, the coat has been considered a static structure providing rigidity and mainly acting as a sieve to exclude exogenous large toxic molecules, such as lytic enzymes. Over recent years, however, new information about the coat’s architecture and function have emerged from experiments using innovative tools such as automated scanning microscopy, and high resolution atomic force microscopy. Principal Findings: Using thin-section electron microscopy, we found that the coat of Bacillus spores has topologically specific proteins forming a layer that is identifiable because it spontaneously becomes decorated with hydrophobic fluorogenic probes from the milieu. Moreover, spores with decorated coat proteins (termed F-spores) have the unexpected attribute of responding to external germination signals by generating intense fluorescence. Fluorescence data from diverse experimental designs, including F-spores constructed from five different Bacilli species, indicated that the fluorogenic ability of F-spores is under control of a putative germination-dependent mechanism. Conclusions: This work uncovers a novel attribute of spore-coat proteins that we exploited to decorate a specific layer imparting germination-dependent fluorogenicity to F-spores. We expect that F-spores will provide a model system to gai

Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two

Surface code quantum computing by lattice surgery

In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.Comment: Published version. 29 pages, 18 figure

A statistical downscaling framework for environmental mapping

In recent years, knowledge extraction from data has become increasingly popular, with many numerical forecasting models, mainly falling into two major categories—chemical transport models (CTMs) and conventional statistical methods. However, due to data and model variability, data-driven knowledge extraction from high-dimensional, multifaceted data in such applications require generalisations of global to regional or local conditions. Typically, generalisation is achieved via mapping global conditions to local ecosystems and human habitats which amounts to tracking and monitoring environmental dynamics in various geographical areas and their regional and global implications on human livelihood. Statistical downscaling techniques have been widely used to extract high-resolution information from regional-scale variables produced by CTMs in climate model. Conventional applications of these methods are predominantly dimensional reduction in nature, designed to reduce spatial dimension of gridded model outputs without loss of essential spatial information. Their downside is twofold—complete dependence on unlabelled design matrix and reliance on underlying distributional assumptions. We propose a novel statistical downscaling framework for dealing with data and model variability. Its power derives from training and testing multiple models on multiple samples, narrowing down global environmental phenomena to regional discordance through dimensional reduction and visualisation. Hourly ground-level ozone observations were obtained from various environmental stations maintained by the US Environmental Protection Agency, covering the summer period (June–August 2005). Regional patterns of ozone are related to local observations via repeated runs and performance assessment of multiple versions of empirical orthogonal functions or principal components and principal fitted components via an algorithm with fully adaptable parameters. We demonstrate how the algorithm can be extended to weather-dependent and other applications with inherent data randomness and model variability via its built-in interdisciplinary computational power that connects data sources with end-users

The Bond-Algebraic Approach to Dualities

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field, and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix representation. Dualities like exact dimensional reduction, emergent, and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the (\mathbb{Z}_2) Higgs model is dual to the extended toric code model {\it in any number of dimensions}. Non-local dual variables and Jordan-Wigner dictionaries are derived from the local mappings of bond algebras. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions.Comment: 131 pages, 22 figures. Submitted to Advances in Physics. Second version including a new section on the eight-vertex model and the correction of several typo

Ataxia-telangiectasia: Linkage analysis in highly inbred Arab and Druze families and differentiation from an ataxia-microcephaly-cataract syndrome

Ataxia-telangiectasia (A-T) is a progressive autosomal recessive disease featuring neurodegeneration, immunodeficiency, chromosomal instability, radiation sensitivity and a highly increased proneness to cancer. A-T is ethnically widespread and genetically heterogeneous, as indicated by the existence of four complementation groups in this disease. Several "A-T-like" genetic diseases share various clinical and cellular characteristics with A-T. By using linkage analysis to study North American and Turkish A-O families, the ATA (A-T, complementation group A) gene has been mapped to chromosome 11q23. A number of Israeli Arab A-T patients coming from large, highly inbred families were assigned to group A In one of these families, an additional autosomal recessive disease was identified, characterized by ataxia, hypotonia, microcephaly and bilateral congenital cataracts. In two patients with this syndrome, normal levels of serum immunoglobulins and alpha-fetoprotein, chromosomal stability in peripheral blood lymphocytes and skin fibroblasts, and normal cellular response to treatments with X-rays and the radiomimetic drug neocarzinostatin indicated that this disease does not share, with A-T, any additional features other than ataxia. These tests also showed that another patient in this family, who is also mentally retarded, is affected with both disorders. This conclusion was further supported by linkage analysis with 11q23 markers. Lod scores between A-O and these markers, cumulated over three large Arab families, were significant and confirmed the localization of the ATA gene to aq23. However, another Druze family unassigned to a specific complementation group, showed several recombinants between A-T and the same markers, leaving the localization of the A-T gene in this family open