Koopman-Hopf Hamilton-Jacobi Reachability and Control

The Hopf formula for Hamilton-Jacobi Reachability analysis has been proposed for solving viscosity solutions of high-dimensional differential games as a space-parallelizeable method. In exchange, however, a complex, potentially non-convex optimization problem must be solved, limiting its application to linear time-varying systems. With the intent of solving Hamilton-Jacobi backwards reachable sets (BRS) and their corresponding online controllers, we pair the Hopf solution with Koopman theory, which can linearize high-dimensional nonlinear systems. We find that this is a viable method for approximating the BRS and performs better than local linearizations. Furthermore, we construct a Koopman-Hopf controller for robustly driving a 10-dimensional, nonlinear, stochastic, glycolysis model and find that it significantly out-competes both stochastic and game-theoretic Koopman-based model predictive controllers against stochastic disturbance

Enrichment and mutation detection of circulating tumor cells from blood samples

The potential of circulating tumor cells (CTCs) in the diagnosis and prognosis of cancer patients has become increasingly attractive. However, molecular analysis of CTCs is hindered by low sensitivity and a high level of background leukocytes in CTC enrichment technologies. We have developed a novel protocol using a microfluidic device, which enriches and retrieves CTCs from blood samples. The principle of CTC capturing is that tumor cells are larger and less deformable than normal blood cells. To evaluate the potential of utilizing Celsee PREP100 in CTC molecular analysis, we prepared prostate cancer cell lines PC3 and LNCaP, retrieved the captured cells and analyzed them using PCR amplicon sequencing. We were able to recover an average of 79% of 110‑1,100 PC3 and 60‑1,500 LNCaP cells, and detect the p.K139fs*3 deletion of the p53 gene in PC3 cells and p.T877A mutation of the androgen receptor gene in LNCaP cells. Next, we spiked these two types of cells into normal donor blood samples, captured the cells and analyzed them using PCR amplicon sequencing. The PC3 and LNCaP cells were captured and retrieved with the ratio of captured CTCs to the background leukocytes reaching 1:1.5 for PC3 and 1:2.9 for LNCaP cells. We further revealed that the p.K139fs*3 deletion and p.T877A mutation can be detected in the captured PC3 and LNCaP cells, respectively. We successfully validated this approach using clinical blood samples from patients with metastatic prostate cancer. Our results demonstrated a novel approach for CTC enrichment and illustrated the potential of CTC molecular characterization for diagnosis, prognosis and treatment selection of patients with metastatic malignancy

Enrichment and mutation detection of circulating tumor cells from blood samples.

The potential of circulating tumor cells (CTCs) in the diagnosis and prognosis of cancer patients has become increasingly attractive. However, molecular analysis of CTCs is hindered by low sensitivity and a high level of background leukocytes in CTC enrichment technologies. We have developed a novel protocol using a microfluidic device, which enriches and retrieves CTCs from blood samples. The principle of CTC capturing is that tumor cells are larger and less deformable than normal blood cells. To evaluate the potential of utilizing Celsee PREP100 in CTC molecular analysis, we prepared prostate cancer cell lines PC3 and LNCaP, retrieved the captured cells and analyzed them using PCR amplicon sequencing. We were able to recover an average of 79% of 110‑1,100 PC3 and 60‑1,500 LNCaP cells, and detect the p.K139fs*3 deletion of the p53 gene in PC3 cells and p.T877A mutation of the androgen receptor gene in LNCaP cells. Next, we spiked these two types of cells into normal donor blood samples, captured the cells and analyzed them using PCR amplicon sequencing. The PC3 and LNCaP cells were captured and retrieved with the ratio of captured CTCs to the background leukocytes reaching 1:1.5 for PC3 and 1:2.9 for LNCaP cells. We further revealed that the p.K139fs*3 deletion and p.T877A mutation can be detected in the captured PC3 and LNCaP cells, respectively. We successfully validated this approach using clinical blood samples from patients with metastatic prostate cancer. Our results demonstrated a novel approach for CTC enrichment and illustrated the potential of CTC molecular characterization for diagnosis, prognosis and treatment selection of patients with metastatic malignancy

Ricci Nilsoliton Black Holes

We follow a constructive approach and find higher-dimensional black holes with Ricci nilsoliton horizons. The spacetimes are solutions to Einstein's equation with a negative cosmological constant and generalises therefore, anti-de Sitter black hole spacetimes. The approach combines a work by Lauret -- which relate so-called Ricci nilsolitons and Einstein solvmanifolds -- and an earlier work by the author. The resulting black hole spacetimes are asymptotically Einstein solvmanifolds and thus, are examples of solutions which are not asymptotically Anti-de Sitter. We show that any nilpotent group in dimension $n\leq 6$ has a corresponding Ricci nilsoliton black hole solution in dimension (n+2). Furthermore, we show that in dimensions (n+2)>8, there exists an infinite number of locally distinct Ricci nilsoliton black hole metrics.Comment: 19 pages; fixed formatting problem

Least-action perihelion precession

The precession of Mercury's perihelion is reinspected by the principle of least action. The anomalous advancement of the apside line that is customarily accounted by the theory of general relativity, is ascribed to the gravitational effect due to the entire Universe. When the least action is written in the Sun's frame of reference, the residual rotation is seen to stem from inertia due to all bodies in the Universe. Since mass corresponds to a bound form of energy, gravity, as any other force, can be described as an energy density difference between a system of bodies and its surrounding energy densities that are dispersed throughout the Universe. According to the principle of least action the Universe is expanding by combustion of mass to radiation in the quest of equilibrating the bound forms of energy with "zero-density surroundings" in least time. Keywords: cosmological principle; energy density; energy dispersal; evolution; gravity; the principle of least actionComment: 7 pages, 3 figure

DARHT-II Injector Transients and the Ferrite Damper

This report summarizes the transient response of the DARHT-II Injector and the design of the ferrite damper. Initial commissioning of the injector revealed a rise time excited 7.8 MHz oscillation on the diode voltage and stalk current leading to a 7.8 MHz modulation of the beam current, position, and energy. Commissioning also revealed that the use of the crowbar to decrease the voltage fall time excited a spectrum of radio frequency modes which caused concern that there might be significant transient RF electric field stresses imposed on the high voltage column insulators. Based on the experience of damping the induction cell RF modes with ferrite, the concept of a ferrite damper was developed to address the crowbar-excited oscillations as well as the rise-time-excited 7.8 MHz oscillations. After the Project decided to discontinue the use of the crowbar, further development of the concept focused exclusively on damping the oscillations excited by the rise time. The design was completed and the ferrite damper was installed in the DARHT-II Injector in February 2006. The organization of this report is as follows. The suite of injector diagnostics are described in Section 2. The data and modeling of the injector transients excited on the rise-time and also by the crowbar are discussed in Section 3; the objective is a concise summary of the present state of understanding. The design of the ferrite damper, and the small scale circuit simulations used to evaluate the ferrite material options and select the key design parameters like the cross sectional area and the optimum gap width, are presented in Section 4. The details of the mechanical design and the installation of the ferrite damper are covered in Section 5. A brief summary of the performance of the ferrite damper following its installation in the injector is presented in Section 6

Metformin Associated With Lower Cancer Mortality in Type 2 Diabetes: ZODIAC-16

OBJECTIVE - Several Studies have suggested an association between specific diabetes treatment and cancer mortality. We studied the association between metformin use and cancer mortality in a prospectively followed cohort. RESEARCH DESIGN AND METHODS - in 1998 and 1999,1,353 patients With type 2 diabetes were enrolled in the Zwolle Outpatient Diabetes project Integrating Available Care 0 (ZODIAC) study in the Netherlands. Vital status was assessed in January 2009. Cancer mortality rate was evaluated using Standardized Mortality ratios (SMRs), and the association between metformin use and cancer mortality was evaluated with a Cox proportional hazards model, taking possible confounders into account. RESULTS - Median follow-up time was 9.6 years, average age at baseline was 68 years, and average A1C was 7.5%. Of the patients, 570 died, of which 122 died of malignancies. The SMR for cancer mortality was 1.47 (95% CI 1.22-1.76). In patients taking metformin compared with patients not taking metformin at baseline, the adjusted hazard ratio (HR) for cancer mortality was 0.43 (95% Cl 0.23-0.80), and the HR With every increase of I g of metformin was 0.58 (95% CI 0.36-093), CONCLUSIONS - in general, patients with type 2 diabetes are at increased risk for cancer mortality. In our group, metformin use was associated with lower cancer mortality compared with nonuse of metformin. Although the design cannot provide a conclusion about causality, our results suggest a protective effect of metformin on cancer mortality

The Case for Healthy U.S.‐China Agricultural Trade Relations despite Deglobalization Pressures

The COVID‐19 pandemic is crippling the global economy and heightening distrust and political disagreements among major countries. Furthermore, ongoing deglobalization efforts taken by firms and countries are fueling the rise of economic nationalism. A prime example is the possible decoupling of US–China economic and trade relations, which the ongoing trade war has already significantly disrupted. This paper analyzes the impacts of COVID‐19 on US agricultural exports to China, especially the added delays and uncertainty regarding China\u27s food imports meeting the US–China phase one trade deal target. I present the views of US farmers and the general public toward China and argue that healthy US–China agricultural trade relations are not only critical for both countries but welcomed by US farmers. I also discuss the possible rise in nontariff barriers following the pandemic as well as trade policies that are increasingly intertwined with political tensions. Finally, I discuss how the US–China phase one trade deal could possibly lead to a more balanced bilateral agricultural trade portfolio with greater share of protein and retail food products

A Unified Approach to Variational Derivatives of Modified Gravitational Actions

Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modified gravitational Lagrangian densities in spacetime dimensions $n\geqslant 3$. We study well-known gravitational actions such as those involving the Gauss-Bonnet and Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic generalizations similar to generic $f(R)$ theories and the algebraic generalization of sixth order gravitational Lagrangians. We put forth a new model involving the gravitational Chern-Simons term and also give three dimensional New massive gravity equations in a new form in terms of the Cotton 2-form

Cosmological Tests of Gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories. The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages --- we summarize these tests and discuss the interesting prospects for new tests in the coming decade.Comment: Invited review for Annals of Physics; 58 pages, 8 figures