Some Methods for Assessing the Need for Non-linear Models in Business Cycle Analysis and Forecasting

There is a long tradition in business cycle analysis of arguing that non-linear models are needed to explain the business cycle. In recent years many non-linear models have been fitted to data on GDP for many countries, but particularly for the U.S. In this paper we set our criteria to evaluate the success of non-linear models in explaining the cycle and then evaluate three recent models in the light of these criteria. We find that the models are capable of explaining the "shape" of expansions, something linear models cannot do, but do so at the cost of making expansions longer than they should be and in producing transition probabilities to recessions that are too low.business cyles, non-linear models

A Covariant Approach To Ashtekar's Canonical Gravity

A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the equations of motion and a symplectic functional two form is constructed which is Lorentz and general co-ordinate invariant. The subtleties and difficulties due to the complex nature of Ashtekar's variables are addressed and resolved.Comment: 18 pages, Plain Te

Mathematical models for vulnerable plaques

A plaque is an accumulation and swelling in the artery walls and typically consists of cells, cell debris, lipids, calcium deposits and fibrous connective tissue. A person is likely to have many plaques inside his/her body even if they are healthy. However plaques may become "vulnerable", "high-risk" or "thrombosis-prone" if the person engages in a high-fat diet and does not exercise regularly. In this study group, we proposed two mathematical models to describe plaque growth and rupture. The first model is a mechanical one that approximately treats the plaque as an inflating elastic balloon. In this model, the pressure inside the core increases and then decreases suggesting that plaque stabilization and prevention of rupture is possible. The second model is a biochemical one that focuses on the role of MMPs in degrading the fibrous plaque cap. The cap stress, MMP concentration, plaque volume and cap thickness are coupled together in a system of phenomenological equations. The equations always predict an eventual rupture since the volume, stresses and MMP concentrations generally grow without bound. The main weakness of the model is that many of the important parameters that control the behavior of the plaque are unknown. The two simple models suggested by this group could serve as a springboard for more realistic theoretical studies. But most importantly, we hope they will motivate more experimental work to quantify some of the important mechanical and biochemical properties of vulnerable plaques

Multi-scale mechanical characterization of highly swollen photo-activated collagen hydrogels

Biological hydrogels have been increasingly sought after as wound dressings or scaffolds for regenerative medicine, owing to their inherent biofunctionality in biological environments. Especially in moist wound healing, the ideal material should absorb large amounts of wound exudate while remaining mechanically competent in situ. Despite their large hydration, however, current biological hydrogels still leave much to be desired in terms of mechanical properties in physiological conditions. To address this challenge, a multi-scale approach is presented for the synthetic design of cyto-compatible collagen hydrogels with tunable mechanical properties (from the nano- up to the macro-scale), uniquely high swelling ratios and retained (more than 70%) triple helical features. Type I collagen was covalently functionalized with three different monomers, i.e. 4-vinylbenzyl chloride, glycidyl methacrylate and methacrylic anhydride, respectively. Backbone rigidity, hydrogen-bonding capability and degree of functionalization (F: 16 ± 12–91 ± 7 mol%) of introduced moieties governed the structure–property relationships in resulting collagen networks, so that the swelling ratio (SR: 707 ± 51–1996 ± 182 wt%), bulk compressive modulus (Ec: 30 ± 7–168 ± 40 kPa) and atomic force microscopy elastic modulus (EAFM: 16 ± 2–387 ± 66 kPa) were readily adjusted. Because of their remarkably high swelling and mechanical properties, these tunable collagen hydrogels may be further exploited for the design of advanced dressings for chronic wound care

Gene expression by marrow stromal cells in a porous collagen-glycosaminoglycan scaffold is affected by pore size and mechanical stimulation.

Marrow stromal cell (MSC) populations, which are a potential source of undifferentiated mesenchymal cells, and culture scaffolds that mimic natural extracellular matrix are attractive options for orthopaedic tissue engineering. A type I collagen-glycosaminoglycan (CG) scaffold that has previously been used clinically for skin regeneration was recently shown to support expression of bone-associated proteins and mineralisation by MSCs cultured in the presence of osteogenic supplements. Here we follow RNA markers of osteogenic differentiation in this scaffold. We demonstrate that transcripts of the late stage markers bone sialoprotein and osteocalcin are present at higher levels in scaffold constructs than in two-dimensional culture, and that considerable gene induction can occur in this scaffold even in the absence of soluble osteogenic supplements. We also find that bone-related gene expression is affected by pore size, mechanical constraint, and uniaxial cyclic strain of the CG scaffold. The data presented here further establish the CG scaffold as a potentially valuable substrate for orthopaedic tissue engineering and for research on the mechanical interactions between cells and their environment, and suggest that a more freely-contracting scaffold with larger pore size may provide an environment more conducive to osteogenesis than constrained scaffolds with smaller pore sizes

Second Order Perturbations in the Randall-Sundrum Infinite Brane-World Model

We discuss the non-linear gravitational interactions in the Randall-Sundrum single brane model. If we naively write down the 4-dimensional effective action integrating over the fifth dimension with the aid of the decomposition with respect to eigen modes of 4-dimensional d'Alembertian, the Kaluza-Klein mode coupling seems to be ill-defined. We carefully analyze second order perturbations of the gravitational field induced on the 3-brane under the assumption of the static and axial-symmetric 5-dimensional metric. It is shown that there remains no pathological feature in the Kaluza-Klein mode coupling after the summation over all different mass modes. Furthermore, the leading Kaluza-Klein corrections are shown to be sufficiently suppressed in comparison with the leading order term which is obtained by the zero mode truncation. We confirm that the 4-dimensional Einstein gravity is approximately recovered on the 3-brane up to second order perturbations.Comment: 15 pages, 2 figures, comment and reference added, typos correcte

Communitarian perspectives on social enterprise

Concepts of social enterprise have been debated repeatedly, and continue to cause confusion. In this paper, a meta-theoretical framework is developed through discussion of individualist and communitarian philosophy. Philosophers from both traditions build social theories that emphasise either consensus (a unitarist outlook) or diversity (a pluralist outlook). The various discourses in corporate governance reflect these assumptions and create four distinct approaches that impact on the relationship between capital and labour. In rejecting the traditional discourse of private enterprise, social enterprises have adopted other approaches to tackle social exclusion, each derived from different underlying beliefs about the purpose of enterprise and the nature of governance. The theoretical framework offers a way to understand the diversity found within the sector, including the newly constituted Community Interest Company (CIC).</p

A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell

Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have represented cytosolic calcium dynamics, while EC migration in angiogenesis has been separately approached with discrete, lattice-based techniques. These two components are here integrated and interfaced to provide a multiscale and hybrid Cellular Potts Model (CPM), where the phenomenology of a motile EC is realistically mediated by its calcium-dependent subcellular events. The model, based on a realistic 3-D cell morphology with a nuclear and a cytosolic region, is set with known biochemical and electrophysiological data. In particular, the resulting simulations are able to reproduce and describe the polarization process, typical of stimulated vascular cells, in various experimental conditions.Moreover, by analyzing the mutual interactions between multilevel biochemical and biomechanical aspects, our study investigates ways to inhibit cell migration: such strategies have in fact the potential to result in pharmacological interventions useful to disrupt malignant vascular progressio

The US stock market leads the Federal funds rate and Treasury bond yields

Using a recently introduced method to quantify the time varying lead-lag dependencies between pairs of economic time series (the thermal optimal path method), we test two fundamental tenets of the theory of fixed income: (i) the stock market variations and the yield changes should be anti-correlated; (ii) the change in central bank rates, as a proxy of the monetary policy of the central bank, should be a predictor of the future stock market direction. Using both monthly and weekly data, we found very similar lead-lag dependence between the S&P500 stock market index and the yields of bonds inside two groups: bond yields of short-term maturities (Federal funds rate (FFR), 3M, 6M, 1Y, 2Y, and 3Y) and bond yields of long-term maturities (5Y, 7Y, 10Y, and 20Y). In all cases, we observe the opposite of (i) and (ii). First, the stock market and yields move in the same direction. Second, the stock market leads the yields, including and especially the FFR. Moreover, we find that the short-term yields in the first group lead the long-term yields in the second group before the financial crisis that started mid-2007 and the inverse relationship holds afterwards. These results suggest that the Federal Reserve is increasingly mindful of the stock market behavior, seen at key to the recovery and health of the economy. Long-term investors seem also to have been more reactive and mindful of the signals provided by the financial stock markets than the Federal Reserve itself after the start of the financial crisis. The lead of the S&P500 stock market index over the bond yields of all maturities is confirmed by the traditional lagged cross-correlation analysis.Comment: 12 pages, 7 figures, 1 tabl