An associative network with spatially organized connectivity

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a network due to the lack of a Hamiltonian, we approach the problem through a signal-to-noise analysis, that we adapt to spatially organized networks. The conditions are analyzed for the appearance of stable, spatially non-uniform profiles of activity with large overlaps with one of the stored patterns. It is also shown, with simulations and analytic results, that the storage capacity does not decrease much when the connectivity of the network becomes short range. In addition, the method used here enables us to calculate exactly the storage capacity of a randomly connected network with arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA

Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Hardy-Carleman Type Inequalities for Dirac Operators

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques

A model problem for the initial-boundary value formulation of Einstein's field equations

In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In particular, they should be compatible with the constraints, yield a well posed initial-boundary value formulation and incorporate some physically desirable properties like, for instance, minimizing reflections of gravitational radiation. Motivated by the problem in General Relativity, we analyze a model problem, consisting of a formulation of Maxwell's equations on a spatially compact region of spacetime with timelike boundaries. The form in which the equations are written is such that their structure is very similar to the Einstein-Christoffel symmetric hyperbolic formulations of Einstein's field equations. For this model problem, we specify a family of Sommerfeld-type constraint-preserving boundary conditions and show that the resulting initial-boundary value formulations are well posed. We expect that these results can be generalized to the Einstein-Christoffel formulations of General Relativity, at least in the case of linearizations about a stationary background.Comment: 25 page

Vacuum Breakdown near a Black Hole Charged by Hypercritical Accretion

We consider a black hole accreting spherically from the surrounding medium. If accretion produces a luminosity close to the Eddington limit the hole acquires a net charge so that electrons and ions can fall with the same velocity. The condition for the electrostatic field to be large enough to break the vacuum near the hole horizon translates into an upper limit for the hole mass, $M\sim 6.6\times 10^{20} {\rm g}.$ The astrophysical conditions under which this phaenomenon can take place are rather extreme, but in principle they could be met by a mini black hole residing at the center of a star.Comment: 6 pages, accepted for publication in the Astrophysical Journa

Just preservation

We are failing to protect the biosphere. Novel views of conservation, preservation, and sustainability are surfacing in the wake of consensus about our failures to prevent extinction or slow climate change. We argue that the interests and well-being of non-humans, youth, and future generations of both human and non-human beings (futurity) have too long been ignored in consensus-based, anthropocentric conservation. Consensus-based stakeholder-driven processes disadvantage those absent or without a voice and allow current adult humans and narrow, exploitative interests to dominate decisions about the use of nature over its preservation for futurity of all life. We propose that authentically non-anthropocentric worldviews that incorporate multispecies justice are needed for a legitimate, deliberative, and truly democratic process of adjudication between competing interests in balancing the preservation and use of nature. Legitimate arenas for such adjudication would be courts that can defend intergenerational equity, which is envisioned by many nations\u27 constitutions, and can consider current and future generations of non-human life. We urge practitioners and scholars to disavow implicit anthropocentric value judgments in their work – or make these transparent and explicit – and embrace a more comprehensive worldview that grants future life on earth fair representation in humanity\u27s decisions and actions today

The elusiveness of old neutron stars

Old neutron stars (ONSs) which have radiated away their internal and rotational energy may still shine if accreting the interstellar medium. Despite their large number, only two promising candidates have been detected so far and rather stringent limits on their observability follow from the analysis of ROSAT surveys. This contrasts with optimistic theoretical estimates that predicted a large number of sources in ROSAT fields. We have reconsidered the issue of ONSs observability, accounting for the spin and magnetic field evolution over the neutron star lifetime. In the framework of a spin-induced field decay model, we show that the total number of ONSs which are, at present, in the accretion stage is reduced by a factor ~5 over previous figures if the characteristic timescale for crustal current dissipation is ~ 10^8 - 10^9 yr. This brings theoretical predictions much closer to observational limits. Most ONSs should be at present in the propeller phase and, if subject to episodic flaring, they could be observable.Comment: 10 pages Latex, 5 ps figures. To be formatted with the AASTeX package. Accepted for publication in Ap

The Neutron Stars Census

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin--down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, $\gtrsim 200-300$ ${\rm km s^{-1}},$ corresponding to a velocity dispersion $\sigma_V\gtrsim 125-190$ km s$^{-1}$. The same conclusion is reached for both a constant magnetic field ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Such high velocities are consistent with those derived from radio pulsar observations. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to less than 1%.Comment: 13 pages, 6 PostScript figures, accepted to Ap

Detection of pulsations and a spectral feature in the X-ray emission of the isolated neutron star 1RXS J214303.7+065419/RBS 1774

We report on the results of a deep XMM-Newton observation of RBS 1774, the most recent dim isolated neutron star candidate found in the ROSAT archive data. Spectral and timing analysis of the high-quality PN and MOS data confirm the association of this source with an isolated neutron star. The spectrum is thermal and blackbody-like, and there is evidence at a significance level > 4sigma that the source is an X-ray pulsar, with spin period of 9.437 s. Spectral fitting reveils the presence of an absorption feature at ~0.7 keV, but at this level data do not have enough resolution to allow us to discriminate between an absorption line or an edge. We compare the newly measured properties of RBS 1774 with those of other known dim isolated neutron stars, and discuss possible interpretations for the absorption feature.Comment: 21 pages, 5 figures, ApJ accepte

X-Ray and UV Orbital Phase Dependence in LMC X-3

The black-hole binary LMC X-3 is known to be variable on time scales of days to years. We investigate X-ray and ultraviolet variability in the system as a function of the 1.7 day binary phase using a 6.4 day observation with the Rossi X-ray Timing Explorer (RXTE) from December 1998. An abrupt 14% flux decrease, lasting nearly an entire orbit, is followed by a return to previous flux levels. This behavior occurs twice, at nearly the same binary phase, but it is not present in consecutive orbits. When the X-ray flux is at lower intensity, a periodic amplitude modulation of 7% is evident in data folded modulo the orbital period. The higher intensity data show weaker correlation with phase. This is the first report of X-ray variability at the orbital period of LMC X-3. Archival RXTE observations of LMC X--3 during a high flux state in December 1996 show similar phase dependence. An ultraviolet light curve obtained with the High Speed Photometer aboard the Hubble Space Telescope shows orbital modulation consistent with that in the optical, caused by the ellipsoidal variation of the spatially deformed companion. The X-ray spectrum of LMC X-3 can be acceptably represented by a phenomenological disk-black-body plus a power law. Changes in the spectrum of LMC X-3 during our observations are compatible with earlier observations during which variations in the 2-10 keV flux are tracked closely by the disk geometry spectral model parameter.Comment: 11 pages, 7 figures, ApJ in pres