Conformal and Nonconformal Symmetries in 2d Dilaton gravity

We study finite-dimensional extra symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting an extra (conformal) symmetry are the models with an exponential potential $V \propto e^{\beta\phi}$ ($S ={1\over2\pi} \int d^2 x \sqrt{-g} [ R \phi + 4 \lambda^2 e^{\beta\phi} ]$), which include the CGHS model as a particular though limiting ($\beta=0$) case. These models give rise to black hole solutions with a mass-dependent temperature. The underlying extra symmetry can be maintained in a natural way in the one-loop effective action, thus implying the exact solubility of the semiclassical theory including back-reaction. Moreover, we also introduce three different classes of (non-conformal) transformations which are extra symmetries for generic 2D dilaton gravity models. Special linear combinations of these transformations turn out to be the (conformal) symmetries of the CGHS and $V \propto e^{\beta\phi}$ models. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an invariant metric, we are able to provide semiclassical models which are also invariant. This generalizes the solvable semiclassical model of Bose, Parker and Peleg (BPP) for a generic 2D dilaton gravity model.Comment: Latex, no figures. Revised version published i

Genomic Alteration Burden in Advanced Prostate Cancer and Therapeutic Implications.

The increasing number of patients with sequenced prostate cancer genomes enables us to study not only individual oncogenic mutations, but also capture the global burden of genomic alterations. Here we review the extent of tumor genome mutations and chromosomal structural variants in various clinical states of prostate cancer, and the related prognostic information. Next, we discuss the underlying mutational processes that give rise to these various alterations, and their relationship to the various molecular subtypes of prostate cancer. Finally, we examine the relationships between the tumor mutation burden of castration-resistant prostate cancer, DNA repair defects, and response to immune checkpoint inhibitor therapy

Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete

We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges. This problem is equivalent to Metric Dimension for Gabriel unit disk graphs. The Gabriel edges of a unit disc graph induce a planar O(\sqrt{n}) distance and an optimal energy spanner. This is one of the most interesting restrictions of Metric Dimension in the context of wireless multi-hop networks.Comment: A brief announcement of this result has been published in the proceedings of ALGOSENSORS 201

Dehydration kinetics and thermochemistry of selected hydrous phases, and simulated gas release pattern in carbonaceous chondrites

As part of our continued program of study on the volatile bearing phases and volatile resource potential of carbonaceous chondrite, results of our experimental studies on the dehydration kinetics of talc as a function of temperature and grain size (50 to 0.5 microns), equilibrium dehydration boundary of talc to 40 kbars, calorimetric study of enthalpy of formation of both natural and synthetic talc as a function of grain size, and preliminary results on the dehydration kinetics of epsomite are reported. In addition, theoretical calculations on the gas release pattern of Murchison meteorite, which is a C2(CM) carbonaceous chondrite, were performed. The kinetic study of talc leads to a dehydration rate constant for 40-50 microns size fraction of k = (3.23 x 10(exp 4))exp(-Q/RT)/min with the activation energy Q = 376 (plus or minus 20) kJ/mole. The dehydration rate was found to increase somewhat with decreasing grain size. The enthalpy of formation of talc from elements was measured to be -5896(10) kJ/mol. There was no measurable effect of grain size on the enthalpy beyond the limits of precision of the calorimetric studies. Also the calorimetric enthalpy of both synthetic and natural talc was found to be essentially the same, within the precision of measurements, although the natural talc had a slightly larger field of stability in our phase equilibrium studies. The high pressure experimental data the dehydration equilibrium of talc (talc = enstatite + coesite + H2O) is in strong disagreement with that calculated from the available thermochemical data, which were constrained to fit the low pressure experimental results. The calculated gas release pattern of Murchison meteorite were in reasonable agreement with that determined by stepwise heating in a gas chromatograph

An associative memory for the on-line recognition and prediction of temporal sequences

This paper presents the design of an associative memory with feedback that is capable of on-line temporal sequence learning. A framework for on-line sequence learning has been proposed, and different sequence learning models have been analysed according to this framework. The network model is an associative memory with a separate store for the sequence context of a symbol. A sparse distributed memory is used to gain scalability. The context store combines the functionality of a neural layer with a shift register. The sensitivity of the machine to the sequence context is controllable, resulting in different characteristic behaviours. The model can store and predict on-line sequences of various types and length. Numerical simulations on the model have been carried out to determine its properties.Comment: Published in IJCNN 2005, Montreal, Canad

Black Hole Evaporation by Thermal Bath Removal

We study the evaporation process of 2D black holes in thermal equilibrium when the incoming radiation is turned off. Our analysis is based on two different classes of 2D dilaton gravity models which are exactly solvable in the semiclassical aproximation including back-reaction. We consider a one parameter family of models interpolating between the Russo-Susskind-Thorlacius and Bose-Parker-Peleg models. We find that the end-state geometry is the same as the one coming from an evaporating black hole formed by gravitational collapse. We also study the quantum evolution of black holes arising in a model with classical action $S = {1\over2\pi} \int d^2x \sqrt{-g} (R\phi + 4\lambda^2e^{\beta\phi})$. The black hole temperature is proportional to the mass and the exact semiclassical solution indicates that these black holes never disappear completely.Comment: LaTeX, psfig.sty. 10 pages. 3 figures (included as PS files

Spin systems with dimerized ground states

In view of the numerous examples in the literature it is attempted to outline a theory of Heisenberg spin systems possessing dimerized ground states (``DGS systems") which comprises all known examples. Whereas classical DGS systems can be completely characterized, it was only possible to provide necessary or sufficient conditions for the quantum case. First, for all DGS systems the interaction between the dimers must be balanced in a certain sense. Moreover, one can identify four special classes of DGS systems: (i) Uniform pyramids, (ii) systems close to isolated dimer systems, (iii) classical DGS systems, and (iv), in the case of $s=1/2$, systems of two dimers satisfying four inequalities. Geometrically, the set of all DGS systems may be visualized as a convex cone in the linear space of all exchange constants. Hence one can generate new examples of DGS systems by positive linear combinations of examples from the above four classes.Comment: With corrections of proposition 4 and other minor change