6 research outputs found

    There are no maximal d.c.e. wtt-degrees

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    В статье доказывается, что не существует максимальной 2-в.п. wtt-степени в 2-в.п. wtt-степеня

    Computability Theory

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    Computability is one of the fundamental notions of mathematics, trying to capture the effective content of mathematics. Starting from Gödel’s Incompleteness Theorem, it has now blossomed into a rich area with strong connections with other areas of mathematical logic as well as algebra and theoretical computer science

    Computability Theory

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    Computability and computable enumerability are two of the fundamental notions of mathematics. Interest in effectiveness is already apparent in the famous Hilbert problems, in particular the second and tenth, and in early 20th century work of Dehn, initiating the study of word problems in group theory. The last decade has seen both completely new subareas develop as well as remarkable growth in two-way interactions between classical computability theory and areas of applications. There is also a great deal of work on algorithmic randomness, reverse mathematics, computable analysis, and in computable structure theory/computable model theory. The goal of this workshop is to bring together researchers representing different aspects of computability theory to discuss recent advances, and to stimulate future work

    The d.r.e wtt-Degrees are Dense

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    © 2019, Springer Nature Switzerland AG. We prove in this paper that the d.r.e. wtt-degrees are dense, improving a result of Wu and Yamaleev. Our result is a direct generalization of Ladner and Sasso’s splitting theorem for r.e. wtt-degrees. One essential feature of our construction is that the Lachlan sets are used as a help to obtain more information of d.r.e. sets

    The d.r.e wtt-Degrees are Dense

    No full text
    © 2019, Springer Nature Switzerland AG. We prove in this paper that the d.r.e. wtt-degrees are dense, improving a result of Wu and Yamaleev. Our result is a direct generalization of Ladner and Sasso’s splitting theorem for r.e. wtt-degrees. One essential feature of our construction is that the Lachlan sets are used as a help to obtain more information of d.r.e. sets

    Improved Orthopaedic Repairs through Mechanically Optimized, Adhesive Biomaterials

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    Despite countless surgical advances over the last several decades refining surgical approaches, repair techniques, and tools to treat tendon and tendon-to-bone injuries, we are still left with repair solutions that rely on fairly crude underlying mechanical principles. Musculoskeletal soft tissues have evolved to transfer high loads by optimizing stress distribution profiles across the tissue at each length scale. However, instead of mimicking these natural load transfer mechanisms, conventional suture approaches are limited by high load transfer across only a small number of anchor points within tissue. This leads to stress concentrations at anchor points that often cause repair failure as the sutures cut longitudinally through the fibrous tendon tissue like a wire cutting through cheese. Most tendon reconstruction ruptures occur within the first several weeks to months after repair, indicating that the initial strength of the repair is critical for its success. Over time under favorable conditions, the healing response can strengthen the repair sufficiently to function under typical physiologic forces. Here, we developed adhesive-based technologies to distribute load transfer more effectively across tendon and tendon-to-bone repairs, thus reducing peak stress and enabling repairs to sustain higher load before failure. First, we hypothesized that using the lateral surfaces along the length of suture to transfer load in shear would improve repair strength. We evaluated the mechanical principles of an adhesive-coated suture using a shear lag model to identify properties of suitable adhesives. Examination of the design space for an optimal adhesive demonstrated requirements for strong adhesion and low stiffness to maximize the strength of the adhesive-coated suture repair construct. When this design space was compared to real material properties in an Ashby plot, the model anticipated theoretical load transfer improvements of more than 7-fold over current tendon suture repairs using optimal elastomeric adhesives. We validated these model predictions experimentally using idealized single-strand pullout tests and clinically relevant flexor tendon repairs in cadaver canine flexor tendon. Clinically relevant repairs performed with Loctite 4903 cyanoacrylate-coated suture had significantly higher strength (17%) compared to standard repairs without adhesive. Notably, cyanoacrylate provided strong adhesion with high stiffness and brittle behavior, and was therefore not an ideal adhesive for enhancing suture repair. Nevertheless, the improvement in repair properties in a clinically relevant setting, even using a non-ideal adhesive, demonstrated the potential for the proposed approach to improve outcomes for treatments requiring suture fixation. We expanded this approach to assess the potential of adhesive films to increase the load tolerance of tendon-to-bone repairs. We hypothesized that adhesive films would redistribute load over the tendon footprint area where tendon inserts into bone, instead of focusing stress at just a few anchor points where suture from bone anchors punctures through tendon. Based on a shear lag model corroborated by a finite element model to establish the limits of the shear lag assumptions for thick or stiff adhesives, desirable adhesives again required compliance and high strength under shear loading. Models predicted an opportunity to increase transfer across tendon-to-bone repairs by over 10-fold. To rapidly evaluate adhesive mechanical properties for both applications using relevant tissue adherends, we developed a new method for consistent lap shear testing using tendon and bone planks. We validated shear lag predictions using this idealized test scenario and further assessed the ability of adhesives to provide additive benefit to rotator cuff repair strength using a clinically relevant human cadaver rotator cuff repair model with and without adhesive. Using this idealized adhesive testing platform, we demonstrated the potential of the proposed approach to improve outcomes in arthroscopic repair settings by applying a catechol-derived, marine mussel-mimetic adhesive with relevant mechanical properties that binds under water. Further study is needed to optimize adhesive binding properties and assess this approach in preclinical surgical tendon-to-bone repair scenarios. Finally, we developed a new approach to deliver adhesives and biofactors in tendon repairs using sutures with a porous outer sheath. These porous sutures were mechanically non-inferior to conventional sutures in single strand tests and clinically relevant tendon repairs. The porosity dramatically increased the suture surface area, which we conjectured would facilitate adhesive interdigitation and strong binding. Furthermore, this porous suture enabled growth factor or other bioactive factor addition to the inside of the suture for increased loading capacity and sustained release over the first 14 days, determined using connective tissue growth factor. In a clinically relevant canine in vivo injury and repair model, we assessed the effects of porous suture delivery of CTGF on the proliferative stage of repair at 14 days. This approach is hypothesized to act as a biological adhesive, increasing repair strength by modulating healing and encouraging tissue ingrowth into the suture pores. Taken together, these technologies represent dramatic departures from the traditional mechanical principles underlying tendon and tendon-to-bone repair, enabling large improvements in surgical repair strength without significantly changing the procedure in the operating room
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