Infinite Matroids and Transfinite Sequences

A matroid is a pair M = (E,I) where E is a set and I is a set of subsets of E that are called independent, echoing the notion of linear independence. One of the leading open problems in infinite matroid theory is the Matroid Intersection Conjecture by Nash-Williams which is a generalization of Hall’s Theorem. In [31] Jerzy Wojciechowski introduced µ- admissibility for pairs of matroids on the same ground set and showed that it is a necessary condition for the existence of a matching. A pair of matroids (M,W) with common ground set E is µ-admissible if a subset of sequences in E × {0,1} have a certain property. In order to determine if this property implies anything about the length of the sequence, we modify µ-admissibility to obtain µ 0 -admissibility, an equivalent property for pairs of matroids. We then use µ 0 -admissibility to show that for every successor ordinal of the form α + 2n there is a pair of partition matroids such that a shortest sequence in E × {0,1} that fails to have the desired property has length α + 2n. Furthermore, we introduce the class of patchwork matroids, which contains all finite matroids and all uniform matroids, and provide a method for their construction, prove a characterization theorem, show the class is closed under duality and taking minors, as well as several other properties. Lastly, a cyclic flat is a flat which is a union of circuits. We combine this notion with that of trees of matroids, which are introduced in [7] to show that the lattice of cyclic flats of a locally finite tree of finite matroids contains an atomic element

Second Harmonic Generation from Phononic Epsilon-Near-Zero Berreman Modes in Ultrathin Polar Crystal Films

Immense optical field enhancement was predicted to occur for the Berreman mode in ultrathin films at frequencies in the vicinity of epsilon near zero (ENZ). Here, we report the first experimental proof of this prediction in the mid-infrared by probing the resonantly enhanced second harmonic generation (SHG) at the longitudinal optic phonon frequency from a deeply subwavelength-thin aluminum nitride (AlN) film. Employing a transfer matrix formalism, we show that the field enhancement is completely localized inside the AlN layer, revealing that the observed SHG signal of the Berreman mode is solely generated in the AlN film. Our results demonstrate that ENZ Berreman modes in intrinsically low-loss polar dielectric crystals constitute a promising platform for nonlinear nanophotonic applications

Does the expansion of a motorway network lead to economic agglomeration? Evidence from China:Evidence from China

In contrast to most existing studies examining the generative effects of transport infrastructure, this paper addresses the distributive effects of transport infrastructure in China. Using panel data from 274 Chinese municipalities in the 2000-2010 period, our study explores the role of motorway network in the evolution of spatial economic agglomerations. Our results confirm the existence of a distributive effect of road infrastructure in China, and show that an improvement in the motorway network leads to a higher degree of geographic concentration of economic activities. However, in our simulation new motorway construction appears to facilitate spatial dispersal when transport costs fall below a critical level. Moreover, the improved road network has led to a loss of industry in China's lagging areas. Accordingly, current transport investment policy, especially in lagging western areas, has not contributed to spatial equity in China, which contrasts with investment in education, for example. (C) 2015 Elsevier Ltd. All rights reserved

Strong Coupling of Epsilon-Near-Zero Phonon Polaritons in Polar Dielectric Heterostructures

We report the first observation of epsilon near zero (ENZ) phonon polaritons in an ultrathin AlN film fully hybridized with surface phonon polaritons (SPhP) supported by the adjacent SiC substrate. Employing a strong coupling model for the analysis of the dispersion and electric field distribution in these hybridized modes, we show that they share the most prominent features of the two precursor modes. The novel ENZ-SPhP coupled polaritons with a highly propagative character and deeply sub-wavelength light confinement can be utilized as building blocks for future infrared and terahertz (THz) nanophotonic integration and communication devices

Evidence for the prepattern/cooption model of vertebrate jaw evolution

The appearance of jaws was a turning point in vertebrate evolution because it allowed primitive vertebrates to capture and process large, motile prey. The vertebrate jaw consists of separate dorsal and ventral skeletal elements connected by a joint. How this structure evolved from the unjointed gill bar of a jawless ancestor is an unresolved question in vertebrate evolution. To understand the developmental bases of this evolutionary transition, we examined the expression of 12 genes involved in vertebrate pharyngeal patterning in the modern jawless fish lamprey. We find nested expression of Dlx genes, as well as combinatorial expression of Msx, Hand and Gsc genes along the dorso-ventral (DV) axis of the lamprey pharynx, indicating gnathostome-type pharyngeal patterning evolved before the appearance of the jaw. In addition, we find that Bapx and Gdf5/6/7, key regulators of joint formation in gnathostomes, are not expressed in the lamprey first arch, whereas Barx, which is absent from the intermediate first arch in gnathostomes, marks this domain in lamprey. Taken together, these data support a new scenario for jaw evolution in which incorporation of Bapx and Gdf5/6/7 into a preexisting DV patterning program drove the evolution of the jaw by altering the identity of intermediate first-arch chondrocytes. We present this “Pre-pattern/Cooption” model as an alternative to current models linking the evolution of the jaw to the de novo appearance of sophisticated pharyngeal DV patterning

Prognostic value of ‘late’ electroencephalography recordings in patients with cardiopulmonal resuscitation after cardiac arrest

Background: Electroencephalography (EEG) significantly contributes to the neuroprognostication after resuscitation from cardiac arrest. Recent studies suggest that the prognostic value of EEG is highest for continuous recording within the first days after cardiac arrest. Early continuous EEG, however, is not available in all hospitals. In this observational study, we sought to evaluate the predictive value of a 'late' EEG recording 5-14 days after cardiac arrest without sedatives. Methods: We retrospectively analyzed EEG data in consecutive adult patients treated at the medical intensive care units (ICU) of the Charite-Universitatsmedizin Berlin. Outcome was assessed as cerebral performance category (CPC) at discharge from ICU, with an unfavorable outcome being defined as CPC 4 and 5. Results: In 187 patients, a 'late' EEG recording was performed. Of these patients, 127 were without continuous administration of sedative agents for at least 24 h before the EEG recording. In this patient group, a continuously suppressed background activity < 10 mu V predicted an unfavorable outcome with a sensitivity of 31% (95% confidence interval (CI) 20-45) and a specificity of 99% (95% CI 91-100). In patients with suppressed background activity and generalized periodic discharges, sensitivity was 15% (95% CI 7-27) and specificity was 100% (95% CI 94-100). GPDs on unsuppressed background activity were associated with a sensitivity of 42% (95% CI 29-46) and a specificity of 92% (95% CI 82-97). Conclusions: A 'late' EEG performed 5 to 14 days after resuscitation from cardiac arrest can aide in prognosticating functional outcome. A suppressed EEG background activity in this time period indicates poor outcome

Dynamic determination of functional liver capacity with the LiMAx test in post‐cardiac arrest patients undergoing targeted temperature management—A prospective trial

Background: Transiently increased transaminases is a common finding after cardiac arrest but little is known about the functional liver capacity (LiMAx) during the post-cardiac arrest syndrome and treatment in the intensive care unit (ICU). The aim of this trial was to evaluate liver function capacity in post-cardiac arrest survivors undergoing targeted temperature management (TTM) in ICU. Methods: Thirty-two post-cardiac arrest survivors were prospectively included with all patients undergoing TTM at 33 degrees C for 24 hours. Blood samples were collected, and LiMAx testing was performed at days 1, 2, 5, and 10 post-cardiac arrest. LiMAx is a non-invasive, in vivo, dynamic breath test determining cytochrome P450 1A2 (CYP1A2) capacity using intravenous (IV) C-13-methacetin, thus reflecting maximum liver function capacity. Static liver parameters were determined and compared to LiMAx values. Results: A typical pattern of transiently, mildly increased transaminases was demonstrated without fulfilling the criteria for hypoxic hepatitis (HH). CYP1A2 activity was reduced with slow normalization over 10 days (lowest median 48 hours after cardiac arrest: 228.5 (25-75 percentile 105.2-301.7 mu g/kg/h, P < .05). Parameters reflecting the liver synthetic function were not impaired, as assessed by, in standard laboratory testing. Conclusion: Liver functional capacity is impaired in patients after cardiac arrest undergoing TTM at 33 degrees C. More data are needed to determine if liver functional capacity may add relevant information, especially in the context of pharmacotherapy, to individualize post-cardiac arrest care