Self-Dual Conformal Supergravity and the Hamiltonian Formulation

In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes include the self-dual spin connection i.e. the Ashtekar connection rather than the triad. The Hamiltonian formulation and the constraints are obtained by using the Dirac-Bergmann algorithm. PACS numbers: 04.20.Cv, 04.20.Fy,04.65.+

Image-guided Radiotherapy to Manage Respiratory Motion: Lung and Liver.

Organ motion as a result of respiratory and cardiac motion poses significant challenges for the accurate delivery of radiotherapy to both the thorax and the upper abdomen. Modern imaging techniques during radiotherapy simulation and delivery now permit better quantification of organ motion, which in turn reduces tumour and organ at risk position uncertainty. These imaging advances, coupled with respiratory correlated radiotherapy delivery techniques, have led to the development of a range of approaches to manage respiratory motion. This review summarises the key strategies of image-guided respiratory motion management with a focus on lung and liver radiotherapy

Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Correlation functions $C(t) \sim$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation \sim\ep leads to a frequency shift \sim \ep C_j. The coalescence of $J$ ($>1$) eigenvectors gives rise to a critical point, which exhibits "giant excess noise" ($C_j \to \infty$). At critical points, the divergent parts of $J$ contributions to $C(t)$ cancel, while time-independent perturbations lead to non-analytic shifts \sim \ep^{1/J}.Comment: REVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism; rewrote Section V E so that it refers to time-dependent (instead of non-equilibrium) effect

Symmetric Hyperbolic System in the Self-dual Teleparallel Gravity

In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity which is equivalent to the Ashtekar formulation is posed. This system is different from the ones in other works by that the reality condition of the spatial metric is included in the symmetric hyperbolicity and then is no longer an independent condition. In addition the constraint equations of this system are rather simpler than the ones in other works.Comment: 8 pages, no figure

Transverse vibration analysis of a prestressed thin circular plate in contact with an acoustic cavity

This paper describes the free transverse vibration analysis of a thin circular plate, subjected to in plane stretching, whilst in interaction with a cylindrical acoustic cavity. An analysis is performed which combines the equations describing the plate and the acoustic cavity to form a matrix equation which, when solved, produces the natural frequencies (latent roots) of the coupled system and associated latent vectors which describe the mode shape coefficients of the plate. After assessing the numerical convergence of the method, results are compared with those from a commercial finite element code (ANSYS). The results analysis is then extended to investigate the effect of stressing upon the free vibration of the coupled system

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft

Torsion and accelerating expansion of the universe in quadratic gravitation

Several exact cosmological solutions of a metric-affine theory of gravity with two torsion functions are presented. These solutions give a essentially different explanation from the one in most of previous works to the cause of the accelerating cosmological expansion and the origin of the torsion of the spacetime. These solutions can be divided into two classes. The solutions in the first class define the critical points of a dynamical system representing an asymptotically stable de Sitter spacetime. The solutions in the second class have exact analytic expressions which have never been found in the literature. The acceleration equation of the universe in general relativity is only a special case of them. These solutions indicate that even in vacuum the spacetime can be endowed with torsion, which means that the torsion of the spacetime has an intrinsic nature and a geometric origin. In these solutions the acceleration of the cosmological expansion is due to either the scalar torsion or the pseudoscalar torsion function. Neither a cosmological constant nor dark energy is needed. It is the torsion of the spacetime that causes the accelerating expansion of the universe in vacuum. All the effects of the inflation, the acceleration and the phase transformation from deceleration to acceleration can be explained by these solutions. Furthermore, the energy and pressure of the matter without spin can produce the torsion of the spacetime and make the expansion of the universe decelerate as well as accelerate.Comment: 20 pages. arXiv admin note: text overlap with gr-qc/0604006, arXiv:1110.344

Feasibility and usability of a regional hub model for colorectal cancer services during the COVID-19 pandemic

The outbreak of the COVID-19 pandemic produced unprecedented challenges, at a global level, in the provision of cancer care. With the ongoing need in the delivery of life-saving cancer treatment, the surgical management of patients with colorectal cancer required prompt significant transformation. The aim of this retrospective study is to report the outcome of a bespoke regional Cancer Hub model in the delivery of elective and essential colorectal cancer surgery, at the height of the first wave of the COVID-19 pandemic. 168 patients underwent colorectal cancer surgery from April 1st to June 30th of 2020. Approximately 75% of patients operated upon underwent colonic resection, of which 47% were left-sided, 34% right-sided and 12% beyond total mesorectal excision surgeries. Around 79% of all resectional surgeries were performed via laparotomy, and the remainder 21%, robotically or laparoscopically. Thirty-day complication rate, for Clavien-Dindo IIIA and above, was 4.2%, and 30-day mortality rate was 0.6%. Re-admission rate, within 30 days post-discharge, was 1.8%, however, no patient developed COVID-19 specific complications post-operatively and up to 28 days post-discharge. The established Cancer Hub offered elective surgical care for patients with colorectal cancer in a centralised, timely and efficient manner, with acceptable post-operative outcomes and no increased risk of contracting COVID-19 during their inpatient stay. We offer a practical model of care that can be used when elective surgery "hubs" for streamlined delivery of elective care needs to be established in an expeditious fashion, either due to the COVID-19 pandemic or any other future pandemics

Modelling and optimal control of blood glucose levels in the human body

Regulating the blood glucose level is a challenging control problem for the human body. Abnormal blood glucose levels can cause serious health problems over time, including diabetes. Although several mathematical models have been proposed to describe the dynamics of glucose-insulin interaction, none of them have been universally adopted by the research community. In this paper, we consider a dynamic model of the blood glucose regulatory system originally proposed by Liu and Tang in 2008. This model consists of eight state variables naturally divided into three subsystems: the glucagon and insulin transition subsystem, the receptor binding subsystem and the glucosesubsystem. The model contains 36 model parameters, many of which are unknown and difficult to determine accurately. We formulate an optimal parameter selection problem in which optimal values for the model parameters must be selected so that the resulting model best its given experimental data.We demonstrate that this optimal parameter selection problem can be solved readily using the optimal control software MISER 3.3. Using this approach, significant improvements can be made in matching the model to the experimental data. We also investigate the sensitivity of the resulting optimizedmodel with respect to the insulin release rate. Finally, we use MISER 3.3 to determine optimal open loop controls for the optimized model

Enhanced ex vivo expansion of adult mesenchymal stem cells by fetal mesenchymal stem cell ECM

Large-scale expansion of highly functional adult human mesenchymal stem cells (aMSCs) remains technologically challenging as aMSCs lose self renewal capacity and multipotency during traditional long-term culture and their quality/quantity declines with donor age and disease. Identification of culture conditions enabling prolonged expansion and rejuvenation would have dramatic impact in regenerative medicine. aMSC-derived decellularized extracellular matrix (ECM) has been shown to provide such microenvironment which promotes MSC self renewal and “stemness”. Since previous studies have demonstrated superior proliferation and osteogenic potential of human fetal MSCs (fMSCs), we hypothesize that their ECM may promote expansion of clinically relevant aMSCs. We demonstrated that aMSCs were more proliferative (∼1.6×) on fMSC-derived ECM than aMSC-derived ECMs and traditional tissue culture wares (TCPS). These aMSCs were smaller and more uniform in size (median ± interquartile range: 15.5 ± 4.1 μm versus 17.2 ± 5.0 μm and 15.5 ± 4.1 μm for aMSC ECM and TCPS respectively), exhibited the necessary biomarker signatures, and stained positive for osteogenic, adipogenic and chondrogenic expressions; indications that they maintained multipotency during culture. Furthermore, fMSC ECM improved the proliferation (∼2.2×), size (19.6 ± 11.9 μm vs 30.2 ± 14.5 μm) and differentiation potential in late-passaged aMSCs compared to TCPS. In conclusion, we have established fMSC ECM as a promising cell culture platform for ex vivo expansion of aMSCs.Singapore-MIT Alliance for Research and Technolog