Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $\omega_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $\omega_m$-dependent optimal frequency $\omega=\omega_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.Comment: 18 pages, 7 figures. The title has been changed with respect to the one in the previous versio

Preventing Incomplete/Hidden Requirements: Reflections on Survey Data from Austria and Brazil

Many software projects fail due to problems in requirements engineering (RE). The goal of this paper is analyzing a specific and relevant RE problem in detail: incomplete/hidden requirements. We replicated a global family of RE surveys with representatives of software organizations in Austria and Brazil. We used the data to (a) characterize the criticality of the selected RE problem, and to (b) analyze the reported main causes and mitigation actions. Based on the analysis, we discuss how to prevent the problem. The survey includes 14 different organizations in Austria and 74 in Brazil, including small, medium and large sized companies, conducting both, plan-driven and agile development processes. Respondents from both countries cited the incomplete/hidden requirements problem as one of the most critical RE problems. We identified and graphically represented the main causes and documented solution options to address these causes. Further, we compiled a list of reported mitigation actions. From a practical point of view, this paper provides further insights into common causes of incomplete/hidden requirements and on how to prevent this problem.Comment: in Proceedings of the Software Quality Days, 201

Mesoscopic non-equilibrium thermodynamics approach to non-Debye dielectric relaxation

Mesoscopic non-equilibrium thermodynamics is used to formulate a model describing non-homogeneous and non-Debye dielectric relaxation. The model is presented in terms of a Fokker-Planck equation for the probability distribution of non-interacting polar molecules in contact with a heat bath and in the presence of an external time-dependent electric field. Memory effects are introduced in the Fokker-Planck description through integral relations containing memory kernels, which in turn are used to establish a connection with fractional Fokker-Planck descriptions. The model is developed in terms of the evolution equations for the first two moments of the distribution function. These equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a functions of the frequency and the wave number. Different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems. For the case of Cole-Cole relaxation, we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt.Comment: 33 pages, 6 figure

XMM-Newton observations of the neutron star X-ray transient KS 1731-260 in quiescence

We report on XMM-Newton observations performed on 2001 September 13-14 of the neutron star X-ray transient KS 1731-260 in quiescence. The source was detected at an unabsorbed 0.5-10 keV flux of only 4 - 8 x 10^{-14} erg/s, depending on the model used to fit the data, which for a distance of 7 kpc implies a 0.5-10 keV X-ray luminosity of approximately 2 - 5 x 10^{32} erg/s. The September 2001 quiescent flux of KS 1731-260 is lower than that observed during the Chandra observation in March 2001. In the cooling neutron star model for the quiescent X-ray emission of neutron star X-ray transients, this decrease in the quiescent flux implies that the crust of the neutron star in KS 1731-260 cooled down rapidly between the two epochs, indicating that the crust has a high conductivity. Furthermore, enhanced cooling in the neutron star core is also favored by our results.Comment: Accepter for publication in ApJ Letters, 22 May 200

A Retrograde Spin of the Black Hole in MAXI J1659–152

We present the results of spectral analysis of the galactic black-hole binary MAXI J1659--152 in the rising phase of the outburst that lasted for about 65 days starting on 2010 September 25. The presence of a broad Fe line, verified by Monte-Carlo simulations, and coverage of a wide energy band by utilizing the combined spectral capabilities of XMM-Newton/EPIC-pn and RXTE/PCA allowed us to use a combination of reflection spectroscopy and continuum fitting methods to estimate the spin of the black hole. We explored the entire parameter range allowed by the present uncertainties on black-hole mass, inclination, and distance as well as the accretion rate. We show that for about 95 percentage of parameter space and very reasonable upper limits on mass accretion rate, the spin of the black hole has to be negative. This is the first clear detection of negative spin in a galactic black-hole binary.Comment: Published in ApJL. 9 pages, 4 figure

Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem

We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions (Dobiski-type formulas) are obtained for these quantities by both algebraic and combinatorial methods. By extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs. This link provides a combinatorial interpretation of the numbers arising in this normal ordering problem.Comment: 10 pages, 5 figure

Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior

A large local rotational speed for the Galaxy found from proper-motions: Implications for the mass of the Milky-Way

Predictions from a Galactic Structure and Kinematic model are compared to the absolute proper-motions of about 30,000 randomly selected stars with $9 < B_{\rm J} \le 19$ derived from the Southern Proper-Motion Program (SPM) toward the South Galactic Pole. The absolute nature of the SPM proper-motions allow us to measure not only the relative motion of the Sun with respect to the local disk, but also, and most importantly, the overall state of rotation of the local disk with respect to galaxies. The SPM data are best fit by models having a solar peculiar motion of +5 km~s$^{-1}$ in the V-component (pointing in the direction of Galactic rotation), a large LSR speed of 270 km~s$^{-1}$, and a disk velocity ellipsoid that points towards the Galactic center. We stress, however, that these results rest crucially on the assumptions of both axisymmetry and equilibrium dynamics. The absolute proper-motions in the U-component indicate a solar peculiar motion of $11.0 \pm 1.5$ km~s$^{-1}$, with no need for a local expansion or contraction term. The implications of the large LSR speed are discussed in terms of gravitational mass of the Galaxy inferred from the most recent and accurate determination for the proper-motion of the LMC. We find that our derived value for the LSR is consistent both with the mass of the Galaxy inferred from the motion of the Clouds ($3 - 4 \times 10^{12} M_\odot$ to $\sim 50$ kpc), as well as the timing argument, based on the binary motion of M31 and the Milky Way, and Leo I and the Milky Way ($\ge 1.2 \times 10^{12} M_\odot$ to $\sim 200$ kpc).Comment: 7 pages (AAS Latex macro v4.0), 2 B&W postscript figures, accepted for publication on ApJ, Letters sectio

The missing link in early emotional processing

Initial evaluation structures (IESs) currently proposed as the earliest detectors of affective stimuli (e.g., amygdala, orbitofrontal cortex, or insula) are high-order structures (a) whose response latency cannot account for the first visual cortex emotion-related response (~80 ms), and (b) lack the necessary infrastructure to locally analyze the visual features that define emotional stimuli. Several thalamic structures accomplish both criteria. The lateral geniculate nucleus (LGN), a first-order thalamic nucleus that actively processes visual information, with the complement of the thalamic reticular nucleus (TRN) are proposed as core IESs. This LGN–TRN tandem could be supported by the pulvinar, a second-order thalamic structure, and by other extrathalamic nuclei. The visual thalamus, scarcely explored in affective neurosciences, seems crucial in early emotional evaluation.This research was supported by the Ministerio de Ciencia e Innovación (MICINN) (Grant no. PGC2018-093570- B-I00) and the Comunidad de Madrid (Grant no. HUM19-HUM5705)