Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

Syntheses, characterization and crystal structures of a new functionalised TTF derivative and its Ni(II) complex

The new ligand 4,5-bis (2-pyridylmethylsulfanyl)-4',5'-bis(cyanoethylthio)tetrathiafulvalene (BPM-BCET-TTF) and its nickel(II) complex have been prepared and crystallographically characterized. The Ni(II) complex shows octahedral geometry around the metal ion with the coordination site occupied by the pyridyl nitrogen atoms, the thioether sulfur atoms of the ligand and cis coordination of the halide ions.

Searching the hearts of graphene-like molecules for simplicity, sensitivity and logic

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons (PAHs) could be isolated and manipulated, then a significant step towards realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

Granular layer in the periplasmic space of gram-positive bacteria and fine structures of Enterococcus gallinarum and Streptococcus gordonii septa revealed by cryo-electron microscopy of vitreous sections.

High-resolution structural information on optimally preserved bacterial cells can be obtained with cryo-electron microscopy of vitreous sections. With the help of this technique, the existence of a periplasmic space between the plasma membrane and the thick peptidoglycan layer of the gram-positive bacteria Bacillus subtilis and Staphylococcus aureus was recently shown. This raises questions about the mode of polymerization of peptidoglycan. In the present study, we report the structure of the cell envelope of three gram-positive bacteria (B. subtilis, Streptococcus gordonii, and Enterococcus gallinarum). In the three cases, a previously undescribed granular layer adjacent to the plasma membrane is found in the periplasmic space. In order to better understand how nascent peptidoglycan is incorporated into the mature peptidoglycan, we investigated cellular regions known to represent the sites of cell wall production. Each of these sites possesses a specific structure. We propose a hypothetic model of peptidoglycan polymerization that accommodates these differences: peptidoglycan precursors could be exported from the cytoplasm to the periplasmic space, where they could diffuse until they would interact with the interface between the granular layer and the thick peptidoglycan layer. They could then polymerize with mature peptidoglycan. We report cytoplasmic structures at the E. gallinarum septum that could be interpreted as cytoskeletal elements driving cell division (FtsZ ring). Although immunoelectron microscopy and fluorescence microscopy studies have demonstrated the septal and cytoplasmic localization of FtsZ, direct visualization of in situ FtsZ filaments has not been obtained in any electron microscopy study of fixed and dehydrated bacteria.

The genetic basis of craniofacial and dental abnormalities

The embryonic head development, including the formation of dental structures, is a complex and delicate process guided by specific genetic programs. Genetic changes and environmental factors can disturb the execution of these programs and result in abnormalities in orofacial and dental structures. Orofacial clefts and hypodontia/ oligodontia are examples of such abnormalities frequently seen in dental clinics. An insight into the mechanisms and genes involved in the formation of orofacial and dental structures has been gradually gained by genetic analysis of families and by the use of experimental vertebrate models such as the mouse and chick models. The development of novel clinical therapies for orofacial and dental pathological conditions depends very much on a detailed knowledge of the molecular and cellular processes that are involved in head formation.

Magnetic resonance imaging for diagnosis and assessment of cartilage defect repairs

Clinical magnetic resonance imaging (MRI) is the method of choice for the non-invasive evaluation of articular cartilage defects and the follow-up of cartilage repair procedures. The use of cartilage-sensitive sequences and a high spatial-resolution technique enables the evaluation of cartilage morphology even in the early stages of disease, as well as assessment of cartilage repair. Sequences that offer high contrast between articular cartilage and adjacent structures, such as the fat-suppressed, 3-dimensional, spoiled gradient-echo sequence and the fast spin-echo sequence, are accurate and reliable for evaluating intrachondral lesions and surface defects of articular cartilage. These sequences can also be performed together in reasonable examination times. In addition to morphology, new MRI techniques provide insight into the biochemical composition of articular cartilage and cartilage repair tissue. These techniques enable the diagnosis of early cartilage degeneration and help to monitor the effect and outcome of various surgical and non-surgical cartilage repair therapies.

Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

Linking Landscape Protection and Nature Conservation: Switzerland’s Experience with Protected Mire Landscapes

Since 1987, Switzerland’s Federal Inventory of Mire Landscapes of Particular Beauty and National Importance has provided an instrument for the integration of nature conservation and landscape protection. Mires and mire landscape protection are strictly regulated. However, research results show that neither the goals of mire protection nor those of mire landscape protection are being achieved. The reasons for this are manifold and, in particular, have to do with a lack of coordination between the various policy areas that shape mire environments and mire landscapes. There are several key challenges involving different political and administrative levels. At the national level, mechanisms must be devised that enable differentiated regional implementation of national sectoral policies. In the context of cantonal structure planning, regional nature conservation and landscape protection priorities should be established based on existing regional potentials vis-à-vis the natural environment and landscapes (including protected biotopes and landscapes). At the regional level (spanning multiple communes), integrated planning instruments and governance structures should be developed so that implementation of national and cantonal sectoral policies may be harmonized under the umbrella of regional and integrated development plans. These adjustments to Switzerland’s institutional system are necessary to enable far-reaching integration of nature conservation and landscape protection when setting regional policy priorities. This would strengthen the protection of mire landscapes and other integrative instruments such as regional nature parks of national importance.

Dynamic intraligamentary stabilization and primary repair: A new concept for the treatment of knee dislocation.

BACKGROUND Traumatic knee dislocation represents a rare but devastating injury. Several controversies persist regarding type of treatment, surgical timing, graft selection, repair versus reconstruction of the medial and lateral structures, surgical techniques and postoperative rehabilitation. A new technique for primary ACL stabilization, dynamic intaligamentary stabilization (DIS) was developed at the authors' institution. The purpose of this study was to analyze the clinical and radiological outcomes of surgically treated traumatic knee dislocations by means of the DIS technique for the ACL, primary suturing for PCL, MCL and LCL. METHODS Between 2009 and 2012, 35 patients treated surgically for traumatic knee dislocation with primary anterior cruciate ligament (ACL) reconstruction with DIS, suturing of the posterior cruciate ligament (PCL) and primary complete repair of collaterals, were evaluated clinically (IKDC score, SF12 health survey, Lysholm score, Tegner score) and radiologically with a mean follow up of 2.2 years (range 1.00-3.50 years) years. Instrumented anterior-posterior translation was measured (KT-2000). RESULTS Anterior/posterior translation (KT-2000) for the healthy and injured limb was 4.8mm (range 3-8mm) and 7.3mm (range 5-10) (89N) respectively. Valgus and varus stress testing in 30° flexion was normal in 26 (75%) and 29 (83%) patients, respectively. The IKDC score was B in 29 (83%) and C in 6 (17%) patients, while the mean Tegner score was 6 (range 4-8). The mean Lysholm score was 90.83 (range 81-95) and mean SF-12 physical and mental scores were 54.1 (range 45-60) and 51.0 (range 39-62) respectively. In 2 patients, a secondary operation was performed. CONCLUSIONS Early, one stage reconstruction with DIS can achieve good functional results and patient satisfaction with overall restoration of sports and working capacity without graft requirements.