On the classification of plane graphs representing structurally stable rational Newton flows

We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufficient conditions -of purely combinatorial nature- for an arbitrary plane graph in order to be topologically equivalent with a Newton graph. Finally, we analyse the structure of Newton graphs and prove the existence of a polynomial algorithm to recognize such graphs

One-parameter families of optimization problems: equality constraints

In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well

On the stratification of a class of specially structured matrices

We consider specially structured matrices representing optimization problems with quadratic objective functions and (finitely many) affine linear equality constraints in an n-dimensional Euclidean space. The class of all such matrices will be subdivided into subsets ['strata'], reflecting the features of the underlying optimization problems. From a differential-topological point of view, this subdivision turns out to be very satisfactory: Our strata are smooth manifolds, constituting a so-called Whitney Regular Stratification, and their dimensions can be explicitly determined. We indicate how, due to Thom's Transversality Theory, this setting leads to some fundamental results on smooth one-parameter families of linear-quadratic optimization problems with ( finitely many) equality and inequality constraints

Critical sets in parametric optimization

We deal with one-parameter families of optimization problems in finite dimensions. The constraints are both of equality and inequality type. The concept of a ‘generalized critical point’ (g.c. point) is introduced. In particular, every local minimum, Kuhn-Tucker point, and point of Fritz John type is a g.c. point. Under fairly weak (even generic) conditions we study the set∑ consisting of all g.c. points. Due to the parameter, the set∑ is pieced together from one-dimensional manifolds. The points of∑ can be divided into five (characteristic) types. The subset of ‘nondegenerate critical points’ (first type) is open and dense in∑ (nondegenerate means: strict complementarity, nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints). A nondegenerate critical point is completely characterized by means of four indices. The change of these indices along∑ is presented. Finally, the Kuhn-Tucker subset of∑ is studied in more detail, in particular in connection with the (failure of the) Mangasarian-Fromowitz constraint qualification

The neutron star soft X-ray transient 1H1905+000 in quiescence

In this Paper we report on our analysis of a ~25 ksec. Chandra X-ray observation of the neutron star soft X-ray transient (SXT) 1H1905+000 in quiescence. Furthermore, we discuss our findings of the analysis of optical photometric observations which we obtained using the Magellan telescope and photometric and spectroscopic observations which we obtained using the Very Large Telescope at Paranal. The X-ray counterpart of 1H1905+000 was not detected in our Chandra data, with a 95 per cent confidence limit to the source count rate of 1.2x10^-4 counts s^-1. For different spectral models this yields an upper limit on the luminosity of 1.8x10^31 erg s^-1 (for an upper limit on the distance of 10 kpc.) This luminosity limit makes 1H1905+000 the faintest neutron star SXT in quiescence observed to date. The neutron star luminosity is so low that it is similar to the lowest luminosities derived for black hole SXTs in quiescence. This low luminosity for a neutron star SXT challanges the hypothesis presented in the literature that black hole SXTs in quiescence have lower luminosities than neutron star SXTs as a result of the presence of a black hole event horizon. Furthermore, the limit on the neutron star luminosity obtained less than 20 years after the outburst has ceased, constrains the thermal conductivity of the neutron star crust. Finally, the neutron star core must be so cold that unless the time averaged mass accretion rate is lower than 2x10^-12 M_sun yr^-1, core cooling has to proceed via enhanced neutrino emission processes. We derive a limit on the absolute I-band magnitude of the quiescent counterpart of M_I>7.8 assuming the source is at 10 kpc. This is in line with 1H1905+000 being an ultra-compact X-ray binary, as has been proposed based on the low outburst V-band absolute magnitude.Comment: 10 pages, 5 figures, accepted for publication in MNRA

A Framework for Formal Modeling and Analysis of Organizations

A new, formal, role-based, framework for modeling and analyzing both real world and artificial organizations is introduced. It exploits static and dynamic properties of the organizational model and includes the (frequently ignored) environment. The transition is described from a generic framework of an organization to its deployed model and to the actual agent allocation. For verification and validation of the proposed model, a set of dedicated techniques is introduced. Moreover, where most computational models can handle only two or three layered organizational structures, our framework can handle any arbitrary number of organizational layers. Henceforth, real-world organizations can be modeled and analyzed, as illustrated by a case study, within the DEAL project line. © Springer Science+Business Media, LLC 2007

Probing the Crust of the Neutron Star in EXO 0748-676

X-ray observations of quiescent X-ray binaries have the potential to provide insight into the structure and the composition of neutron stars. EXO 0748-676 had been actively accreting for over 24 yr before its outburst ceased in late 2008. Subsequent X-ray monitoring revealed a gradual decay of the quiescent thermal emission that can be attributed to cooling of the accretion-heated neutron star crust. In this work, we report on new Chandra and Swift observations that extend the quiescent monitoring to ~5 yr post-outburst. We find that the neutron star temperature remained at ~117 eV between 2009 and 2011, but had decreased to ~110 eV in 2013. This suggests that the crust has not fully cooled yet, which is supported by the lower temperature of ~95 eV that was measured ~4 yr prior to the accretion phase in 1980. Comparing the data to thermal evolution simulations reveals that the apparent lack of cooling between 2009 and 2011 could possibly be a signature of convection driven by phase separation of light and heavy nuclei in the outer layers of the neutron star.Comment: 9 pages, 4 tables, 3 figures. Minor revisions according to referee report. Accepted to Ap

Chandra and Swift observations of the quasi-persistent neutron star transient EXO 0748-676 back to quiescence

The quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748-676 recently started the transition to quiescence following an accretion outburst that lasted more than 24 years. We report on two Chandra and twelve Swift observations performed within five months after the end of the outburst. The Chandra spectrum is composed of a soft, thermal component that fits to a neutron star atmosphere model with kT^inf~0.12 keV, joined by a hard powerlaw tail that contributes ~20% of the total 0.5-10 keV unabsorbed flux. The combined Chandra/Swift data set reveals a relatively hot and luminous quiescent system with a temperature of kT^inf~0.11-0.13 keV and a bolometric thermal luminosity of ~8.1E33-1.6E34 (d/7.4 kpc)^2 erg/s. We discuss our results in the context of cooling neutron star models.Comment: Accepted for publication in MNRAS Letters, moderate revision according to referee report, added one plot to figure 2 and included new Swift observations, 5 pages, 2 figure