Balian-Low Theorems in Several Variables

Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $\mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the Quantitative BLT, proving in particular nonsymmetric BLTs in both the discrete and continuous setting for functions with more than one argument. Finally, in direct analogy of the continuous setting, we show the Quantitative Finite BLT implies the Finite BLT.Comment: To appear in Approximation Theory 16 conference proceedings volum

Prime tight frames

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two

Graphical Approach to Model Reduction for Nonlinear Biochemical Networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a “concentration-clamp” procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β1-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal “kinetic biomarkers” of the overall β1-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems

Development and characterisation of a large diameter decellularised vascular allograft

The aims of this study were to develop a biological large diameter vascular graft by decellularisation of native human aorta to remove the immunogenic cells whilst retaining the essential biomechanical, and biochemical properties for the ultimate benefit of patients with infected synthetic grafts. Donor aortas (n = 6) were subjected to an adaptation of a propriety decellularisation process to remove the cells and acellularity assessed by histological analysis and extraction and quantification of total DNA. The biocompatibility of the acellular aortas was determined using standard contact cytotoxicity tests. Collagen and denatured collagen content of aortas was determined and immunohistochemistry was used to determine the presence of specific extracellular matrix proteins. Donor aortas (n = 6) were divided into two, with one half subject to decellularisation and the other half retained as native tissue. The native and decellularised aorta sections were then subject to uniaxial tensile testing to failure [axial and circumferential directions] and suture retention testing. The data was compared using a paired t-test. Histological evaluation showed an absence of cells in the treated aortas and retention of histoarchitecture including elastin content. The decellularised aortas had less than 15 ng mg¯¹ total DNA per dry weight (mean 94% reduction) and were biocompatible as determined by in vitro contact cytotoxicity tests. There were no gross changes in the histoarchitecture [elastin and collagen matrix] of the acellular aortas compared to native controls. The decellularisation process also reduced calcium deposits within the tissue. The uniaxial tensile and suture retention testing revealed no significant differences in the material properties (p > 0.05) of decellularised aorta. The decellularisation procedure resulted in minimal changes to the biological and biomechanical properties of the donor aortas. Acellular donor aorta has excellent potential for use as a large diameter vascular graft

The Effect of Tear Supplementation on Ocular Surface Sensations during the Interblink Interval in Patients with Dry Eye.

PURPOSE: To investigate the characteristics of ocular surface sensations and corneal sensitivity during the interblink interval before and after tear supplementation in dry eye patients. METHODS: Twenty subjects (41.88+/-14.37 years) with dry eye symptoms were included in the dry eye group. Fourteen subjects (39.13+/-11.27 years) without any clinical signs and/or symptoms of dry eye were included in the control group. Tear film dynamics was assessed by non-invasive tear film breakup time (NI-BUT) in parallel with continuous recordings of ocular sensations during forced blinking. Corneal sensitivity to selective stimulation of corneal mechano-, cold and chemical receptors was assessed using a gas esthesiometer. All the measurements were made before and 5 min after saline and hydroxypropyl-guar (HP-guar) drops. RESULTS: In dry eye patients the intensity of irritation increased rapidly after the last blink during forced blinking, while in controls there was no alteration in the intensity during the first 10 sec followed by an exponential increase. Irritation scores were significantly higher in dry eye patients throughout the entire interblink interval compared to controls (p0.05). CONCLUSION: Ocular surface irritation responses due to tear film drying are considerably increased in dry eye patients compared to normal subjects. Although tear supplementation improves the protective tear film layer, and thus reduce unpleasant sensory responses, the rapid rise in discomfort is still maintained and might be responsible for the remaining complaints of dry eye patients despite the treatment

Railway Systems and the 'Universal Good of the State': Technologies of Government in the 19th-Century Papal State

Informed by Foucault’s concept of governmentality, the paper focuses on nineteenth-century General Commissariat for the Railroad Industry in the Papal State. Unlike in liberal States, where government intervention in the affairs of railway companies was limited, the pressing need to reinforce the Pope’s pastoral power, strengthen the bond between the believers and the Holy See and ensure equity and the efficiency of the new infrastructure meant that the Commissariat acted as a governmental centre of calculation. Accounting technologies in the form of budgets, cost accounting systems and penetrating audits enabled the government to intervene in the operations of private railway companies. The study analyses the role of accounting and auditing practices in the pursuit of non-liberal goals in an industry which is traditionally perceived as critical to the development of a liberal economy, one in which accounting was traditionally used to maintain investors’ confidence in the capitalist system

Staphylococcus aureus Induces Eosinophil Cell Death Mediated by α-hemolysin

Staphylococcus aureus, a major human pathogen, exacerbates allergic disorders, including atopic dermatitis, nasal polyps and asthma, which are characterized by tissue eosinophilia. Eosinophils, via their destructive granule contents, can cause significant tissue damage, resulting in inflammation and further recruitment of inflammatory cells. We hypothesised that the relationship between S. aureus and eosinophils may contribute to disease pathology. We found that supernatants from S. aureus (SH1000 strain) cultures cause rapid and profound eosinophil necrosis, resulting in dramatic cell loss within 2 hours. This is in marked contrast to neutrophil granulocytes where no significant cell death was observed (at equivalent dilutions). Supernatants prepared from a strain deficient in the accessory gene regulator (agr) that produces reduced levels of many important virulence factors, including the abundantly produced α-hemolysin (Hla), failed to induce eosinophil death. The role of Hla in mediating eosinophil death was investigated using both an Hla deficient SH1000-modified strain, which did not induce eosinophil death, and purified Hla, which induced concentration-dependent eosinophil death via both apoptosis and necrosis. We conclude that S. aureus Hla induces aberrant eosinophil cell death in vitro and that this may increase tissue injury in allergic disease