A saturation property of structures obtained by forcing with a compact family of random variables

A method how to construct Boolean-valued models of some fragments of arithmetic was developed in Krajicek (2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family (called compactness in K.(2011)) the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types.Comment: preprint February 201

Random l-colourable structures with a pregeometry

We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: 1. A zero-one law. 2. The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. 3. There is a formula $\xi(x,y)$ (not directly speaking about colours) such that, with asymptotic probability 1, the relation "there is an $l$-colouring which assigns the same colour to $x$ and $y$" is defined by $\xi(x,y)$. 4. With asymptotic probability 1, an $l$-colourable structure has a unique $l$-colouring (up to permutation of the colours).Comment: 35 page

Prototyping Operational Autonomy for Space Traffic Management

Current state of the art in Space Traffic Management (STM) relies on a handful of providers for surveillance and collision prediction, and manual coordination between operators. Neither is scalable to support the expected 10x increase in spacecraft population in less than 10 years, nor does it support automated manuever planning. We present a software prototype of an STM architecture based on open Application Programming Interfaces (APIs), drawing on previous work by NASA to develop an architecture for low-altitude Unmanned Aerial System Traffic Management. The STM architecture is designed to provide structure to the interactions between spacecraft operators, various regulatory bodies, and service suppliers, while maintaining flexibility of these interactions and the ability for new market participants to enter easily. Autonomy is an indispensable part of the proposed architecture in enabling efficient data sharing, coordination between STM participants and safe flight operations. Examples of autonomy within STM include syncing multiple non-authoritative catalogs of resident space objects, or determining which spacecraft maneuvers when preventing impending conjunctions between multiple spacecraft. The STM prototype is based on modern micro-service architecture adhering to OpenAPI standards and deployed in industry standard Docker containers, facilitating easy communication between different participants or services. The system architecture is designed to facilitate adding and replacing services with minimal disruption. We have implemented some example participant services (e.g. a space situational awareness provider/SSA, a conjunction assessment supplier/CAS, an automated maneuver advisor/AMA) within the prototype. Different services, with creative algorithms folded into then, can fulfil similar functional roles within the STM architecture by flexibly connecting to it using pre-defined APIs and data models, thereby lowering the barrier to entry of new players in the STM marketplace. We demonstrate the STM prototype on a multiple conjunction scenario with multiple maneuverable spacecraft, where an example CAS and AMA can recommend optimal maneuvers to the spacecraft operators, based on a predefined reward function. Such tools can intelligently search the space of potential collision avoidance maneuvers with varying parameters like lead time and propellant usage, optimize a customized reward function, and be implemented as a scheduling service within the STM architecture. The case study shows an example of autonomous maneuver planning is possible using the API-based framework. As satellite populations and predicted conjunctions increase, an STM architecture can facilitate seamless information exchange related to collision prediction and mitigation among various service applications on different platforms and servers. The availability of such an STM network also opens up new research topics on satellite maneuver planning, scheduling and negotiation across disjoint entities

Enhanced oxygen solubility in metastable water under tension

Despite its relevance in numerous natural and industrial processes, the solubility of molecular oxygen has never been directly measured in capillary condensed liquid water. In this article, we measure oxygen solubility in liquid water trapped within nanoporous samples, in metastable equilibrium with a subsaturated vapor. We show that solubility increases two-fold at moderate subsaturations (RH ~ 0.55). This evolution with relative humidity is in good agreement with a simple thermodynamic prediction using properties of bulk water, previously verified experimentally at positive pressure. Our measurement thus verifies the validity of this macroscopic thermodynamic theory to strong confinement and large negative pressures, where ignificant non-idealities are expected. This effect has strong implications for important oxygen-dependent chemistries in natural and technological contexts.Comment: Accepted for publication in Langmui

Tameness of holomorphic closure dimension in a semialgebraic set

Given a semianalytic set S in a complex space and a point p in S, there is a unique smallest complex-analytic germ at p which contains the germ of S, called the holomorphic closure of S at p. We show that if S is semialgebraic then its holomorphic closure is a Nash germ, for every p, and S admits a semialgebraic filtration by the holomorphic closure dimension. As a consequence, every semialgebraic subset of a complex vector space admits a semialgebraic stratification into CR manifolds satisfying a strong version of the condition of the frontier.Comment: Published versio

Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..Comment: 33 pages, this version coincides with the published on

An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace transform theory. As an application we offer a free of contradictions alternative in the framework of our algebra of generalized functions. The article is aimed at mathematicians, physicists and engineers who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page

Revision rates after primary hip and knee replacement in England between 2003 and 2006

<b>Background</b>: Hip and knee replacement are some of the most frequently performed surgical procedures in the world. Resurfacing of the hip and unicondylar knee replacement are increasingly being used. There is relatively little evidence on their performance. To study performance of joint replacement in England, we investigated revision rates in the first 3 y after hip or knee replacement according to prosthesis type. <b>Methods and Findings</b>: We linked records of the National Joint Registry for England and Wales and the Hospital Episode Statistics for patients with a primary hip or knee replacement in the National Health Service in England between April 2003 and September 2006. Hospital Episode Statistics records of succeeding admissions were used to identify revisions for any reason. 76,576 patients with a primary hip replacement and 80,697 with a primary knee replacement were included (51% of all primary hip and knee replacements done in the English National Health Service). In hip patients, 3-y revision rates were 0.9% (95% confidence interval [CI] 0.8%–1.1%) with cemented, 2.0% (1.7%–2.3%) with cementless, 1.5% (1.1%–2.0% CI) with “hybrid” prostheses, and 2.6% (2.1%–3.1%) with hip resurfacing (p < 0.0001). Revision rates after hip resurfacing were increased especially in women. In knee patients, 3-y revision rates were 1.4% (1.2%–1.5% CI) with cemented, 1.5% (1.1%–2.1% CI) with cementless, and 2.8% (1.8%–4.5% CI) with unicondylar prostheses (p < 0.0001). Revision rates after knee replacement strongly decreased with age. <b>Interpretation</b>: Overall, about one in 75 patients needed a revision of their prosthesis within 3 y. On the basis of our data, consideration should be given to using hip resurfacing only in male patients and unicondylar knee replacement only in elderly patients

Cinematic and aesthetic cartographies of subjective mutation

This article exmaines the use of cinema as a mapping of subjective mutation in the work of Deleuze, Gauttari and Berardi. Drawing on Deleuze's distinciton between the reduction of the art-work to the symptom and the idea of art as symptomatology, the article focuses on Berardi's use of cinematic examples, posing the quesiton in each case of to what extent they function as symptomatologies or mere symptoms of cultural and subjective mutations in examples ranging from Bergman's Persona to Van Sant's Elephant to finish on speculations about Fincher's The Social Network as a cirtical engagement with subjective mutation in the 21st Century

Medical Data Architecture Project Status

The Medical Data Architecture (MDA) project supports the Exploration Medical Capability (ExMC) risk to minimize or reduce the risk of adverse health outcomes and decrements in performance due to in-flight medical capabilities on human exploration missions. To mitigate this risk, the ExMC MDA project addresses the technical limitations identified in ExMC Gap Med 07: We do not have the capability to comprehensively process medically-relevant information to support medical operations during exploration missions. This gap identifies that the current in-flight medical data management includes a combination of data collection and distribution methods that are minimally integrated with on-board medical devices and systems. Furthermore, there are a variety of data sources and methods of data collection. For an exploration mission, the seamless management of such data will enable a more medically autonomous crew than the current paradigm. The medical system requirements are being developed in parallel with the exploration mission architecture and vehicle design. ExMC has recognized that in order to make informed decisions about a medical data architecture framework, current methods for medical data management must not only be understood, but an architecture must also be identified that provides the crew with actionable insight to medical conditions. This medical data architecture will provide the necessary functionality to address the challenges of executing a self-contained medical system that approaches crew health care delivery without assistance from ground support. Hence, the products supported by current prototype development will directly inform exploration medical system requirements