Reverse engineering small 4-manifolds

We introduce a general procedure called `reverse engineering' that can be used to construct infinite families of smooth 4-manifolds in a given homeomorphism type. As one of the applications of this technique, we produce an infinite family of pairwise nondiffeomorphic 4-manifolds homeomorphic to CP^2#3(-CP^2).Comment: 13 pages, 2 figures. This is the final version published in AGT, volume 7 (2007), pp. 2103-2116

Comprehending environmental and economic sustainability: Comparative analysis of stability principles in the biosphere and free market economy

Using the formalism of Lyapunov potential function it is shown that the stability principles for biomass in the ecosystem and for employment in economics are mathematically similar. The ecosystem is found to have a stable and an unstable stationary state with high (forest) and low (grasslands) biomass, respectively. In economics, there is a stable stationary state with high employment, which corresponds to mass production of conventional goods sold at low cost price, and an unstable stationary state with lower employment, which corresponds to production of novel goods appearing in the course of technological progress. An additional stable stationary state is described for economics, the one corresponding to very low employment in production of life essentials such as energy and raw materials. In this state the civilization currently pays 10% of global GDP for energy produced by a negligible minority of the working population (currently ~0.2%) and sold at prices greatly exceeding the cost price by 40 times. It is shown that economic ownership over energy sources is equivalent to equating measurable variables of different dimensions (stores and fluxes), which leads to effective violation of the laws of energy and matter conservation.Comment: 51 pages, 6 figure

Time Scales in Long GRBs

We analyze a sample of bright long bursts and find that the pulses duration have a lognormal distribution while the intervals between pulses have an excess of long intervals (relative to lognormal distribution). This excess can be explained by the existence of quiescent times, long periods with no signal above the background. The lognormal distribution of the intervals (excluding the quiescent times) is similar to the distribution of the pulses width. This result suggests that the quiescent times are made by a different mechanism than the rest of the intervals. It also suggests that the intervals (excluding the quiescent times) and the pulse width are connected to the same parameters of the source. We find that there is a correlation between a pulse width and the duration of the interval preceding it. There is a weaker, but still a significant, correlation between a pulse width and the interval following it. The significance of the correlation drops substantially when the intervals considered are not adjacent to the pulse.Comment: 5 pages, 8 figures, accepted for publication by MNRA

Cats with thermal burn injuries from California wildfires show echocardiographic evidence of myocardial thickening and intracardiac thrombi.

Recent increases in the prevalence and severity of wildfires in some regions have resulted in an increased frequency of veterinary burn patients. Few studies exist regarding diagnostics and management of burn wounds in veterinary patients and current knowledge is extrapolated from human literature and research models. Post-burn cardiac injury is a common finding and predictor of mortality in human patients and echocardiography is an important tool in monitoring response to therapy and predicting outcome. We describe the notable findings from cats naturally exposed to California wildfires in 2017 and 2018. Domestic cats (n = 51) sustaining burn injuries from the Tubbs (2017) and Camp (2018) wildfires were prospectively enrolled and serial echocardiograms and cardiac troponin I evaluations were performed. Echocardiograms of affected cats revealed a high prevalence of myocardial thickening (18/51) and spontaneous echocardiographic contrast and thrombi formation (16/51). Forty-two cats survived to discharge and 6 died or were euthanized due to a possible cardiac cause. For the first time, we describe cardiovascular and coagulation effects of thermal burn and smoke inhalation in cats. Further studies in veterinary burn victims are warranted and serve as a translational research opportunity for uncovering novel disease mechanisms and therapies

The Power Spectra of Two Classes of Long-duration Gamma-ray Bursts

We have studied the averaged power density spectra (PDSs) of two classes of long-duration gamma-ray bursts in the recent classification by Balastegui et al.(2001) based on neural network analysis. Both PDSs follow a power law over a wide frequency range with approximately the same slope, which indicates that a process with a self-similar temporal property may underlie the emission mechanisms of both. The two classes of bursts are divided into groups according to their brightness and spectral hardness respectively and each group's PDS was calculated; For both classes, the PDS is found to flatten both with increasing burst brightness and with increasing hardness.Comment: 6 pages, 3 figures, a translated version from published in the Acta Astronomica Sinica, to appear in the Chinese Astronomy & Astrophysics Vol.27, Issue

Product Formulae for Ozsvath-Szabo 4-manifold Invariants

We give formulae for the Ozsvath-Szabo invariants of 4-manifolds X obtained by fiber sum of two manifolds M_1, M_2 along surfaces S_1, S_2 having trivial normal bundle and genus g>0. The formulae follow from a general theorem on the Ozsvath-Szabo invariants of the result of gluing two 4-manifolds along a common boundary, which is phrased in terms of relative invariants of the pieces. These relative invariants take values in a version of Heegaard Floer homology with coefficients in modules over certain Novikov rings; the fiber sum formula follows from the theorem that this "perturbed" version of Heegaard Floer theory recovers the usual Ozsvath-Szabo invariants, when the 4-manifold in question has b^+>1. The construction allows an extension of the definition of the Ozsvath-Szabo invariants to 4-manifolds having b^+ = 1 depending on certain choices, in close analogy with Seiberg-Witten theory. The product formulae lead quickly to calculations of the Ozsvath-Szabo invariants of various 4-manifolds; in all cases the results are in accord with the conjectured equivalence between the Ozsvath-Szabo and Seiberg-Witten invariants.Comment: 70 pages, 2 figure

A Disc-Corona Model for a Rotating Black Hole

We propose a disc-corona model in which a geometrically thin, optically thick disc surrounds a Kerr black hole, and magnetic fields exert a time-steady torque on the inner edge of the accretion disc. The analytical expression of the total gravitational power is derived from the thin-disc dynamics equations by using this new boundary condition. It is shown that the magnetic torque can considerably enhance the amount of energy released in the disc-corona system. Furthermore, the global solutions of this disc-corona system are obtained numerically. We find that the fraction of the power dissipated into the corona in the total for such disc-corona system increases with the increasing dimensionless black hole spin parameter $a_\ast$, but is insensitive on the $\Delta \varepsilon$ which is the additional radiative efficiency parameter relevant to magnetic torque, for $\Delta\varepsilon > 1$. In addition, the emerged spectra from this disc-corona system are simulated by using Monte-Carlo method, and the effect of the different parameters on the output spectra is discussed

Detecting stealthy cyberattacks on adaptive cruise control vehicles: A machine learning approach

With the advent of vehicles equipped with advanced driver-assistance systems, such as adaptive cruise control (ACC) and other automated driving features, the potential for cyberattacks on these automated vehicles (AVs) has emerged. While overt attacks that force vehicles to collide may be easily identified, more insidious attacks, which only slightly alter driving behavior, can result in network-wide increases in congestion, fuel consumption, and even crash risk without being easily detected. To address the detection of such attacks, we first present a traffic model framework for three types of potential cyberattacks: malicious manipulation of vehicle control commands, false data injection attacks on sensor measurements, and denial-of-service (DoS) attacks. We then investigate the impacts of these attacks at both the individual vehicle (micro) and traffic flow (macro) levels. A novel generative adversarial network (GAN)-based anomaly detection model is proposed for real-time identification of such attacks using vehicle trajectory data. We provide numerical evidence {to demonstrate} the efficacy of our machine learning approach in detecting cyberattacks on ACC-equipped vehicles. The proposed method is compared against some recently proposed neural network models and observed to have higher accuracy in identifying anomalous driving behaviors of ACC vehicles