Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient

We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.Comment: 12 pages, 2 table

An X-ray and Infrared Survey of the Lynds 1228 Cloud Core

The nearby Lynds 1228 (L1228) dark cloud at a distance of ~200 pc is known to harbor several young stars including the driving sources of the giant HH 199 and HH 200 Herbig-Haro outflows. L1228 has been previously studied at optical, infrared, and radio wavelengths but not in X-rays. We present results of a sensitive 37 ks Chandra ACIS-I X-ray observation of the L1228 core region. Chandra detected 60 X-ray sources, most of which are faint (<40 counts) and non-variable. Infrared counterparts were identified for 53 of the 60 X-ray sources using archival data from 2MASS, Spitzer, and WISE. Object classes were assigned using mid-IR colors for those objects with complete photometry, most of which were found to have colors consistent with extragalactic background sources. Seven young stellar object (YSO) candidates were identified including the class I protostar HH 200-IRS which was detected as a faint hard X-ray source. No X-ray emission was detected from the luminous protostar HH 199-IRS. We summarize the X-ray and infrared properties of the detected sources and provide IR spectral energy distribution modeling of high-interest objects including the protostars driving the HH outflows.Comment: 38 pages, 7 tables, 8 figures; to appear in A

The role of regulation in influencing income-generating activities among public sector doctors in Peru.

OBJECTIVE: To examine in Peru the nature of dual practice (doctors holding two jobs at once - usually public sector doctors with private practices), the factors that influence individuals' decisions to undertake dual practice, the conditions faced when doing so and the potential role of regulatory intervention in this area. METHODS: The study entailed qualitative interviews with a sample of twenty medical practitioners based in metropolitan Lima, representing a cross-section of those primarily employed in either the private or public sectors and engaged in clinical practice or policy making. The interviews focused on: 1. individuals' experience with dual practice; 2. the general underlying pressures that influence the nature and extent of such activities; and 3. attitudes toward, and the influence of, regulation on such activities. RESULTS: Dual practice is an activity that is widespread and well-accepted, and the prime personal motivation is financial. However, there are also a number of important broad macroeconomic influences on dual practice particularly the oversupply of medical services, the deregulated nature of this market, and the economic crisis throughout the country, which combine to create major hardships for those attempting to make a living through medical practice. There is some support among doctors for tighter regulation. CONCLUSION: Research findings suggest appropriate policy responses to dual practice involve tighter controls on the supply of medical practitioners; alleviation of financial pressures brought by macro-economic conditions; and closer regulation of such activities to ensure some degree of collective action over quality and the maintenance of professional reputations. Further research into this issue in rural areas is needed to ascertain the geographical generalizability of these policy responses

State Law, the Westfall Act, and the Nature of the \u3ci\u3eBivens\u3c/i\u3e Question

In a number of recent cases touching to varying degrees on national security, different courts of appeals have applied a strong presumption against recognition of a Bivens cause of action. In each of these cases, the courts’ approach was based on the belief that the creation of a cause of action is a legislative function and that the courts would be usurping Congress’s role if they recognized a Bivens action without legislative authorization. Thus, faced with a scenario where they believed that the remedial possibilities were either Bivens or nothing, these courts of appeals chose nothing. The concerns that led these courts to decline to recognize a Bivens action, if truly implicated by these cases, would be reasons to bar the suits from the courts altogether. In contrast, as we explain in this essay, the Bivens question was at least initially understood as whether a federal cause of action should supplement existing state law remedies. Thus, these recent lower-court decisions reveal a fundamental misapprehension about the intended relationship between Bivens and state law. So understood, and as courts have already recognized in other contexts, the very concerns relied upon in these recent national security cases would, if anything, have traditionally supported a federal remedial regime rather than one under state law. As the Supreme Court\u27s recent decision in Minneci v. Pollard illustrates, the principal reason to disfavor recognition of Bivens remedies should be the availability of adequate remedies under state law, and not a desire to immunize the relevant officers from any liability whatsoever. Thus, unlike these recent cases, decisions not to recognize a Bivens remedy should leave the plaintiff free to pursue whatever recourse state law may provide. Although this view of Bivens was generally shared by both its supporters and detractors when it was decided, it has receded from view largely thanks to the Westfall Act, which most courts and commentators today read as preempting all state-law tort claims against federal officers acting within the scope of their employment. In our view, this conclusion reflects a surprising misreading of the Act, which specifically exempts from its preemption provision any claim which is brought for a violation of the Constitution of the United States, presumably including non-federal tort claims grounded on federal constitutional violations. Indeed, given that the legislative history of the Westfall Act suggests that Congress merely sought to preserve the status quo, it is odd to read the statute as dramatically altering the nature and consequences of the Bivens question. Nevertheless, if the Westfall Act does indeed have this effect, we conclude that it should therefore significantly strengthen the argument for recognizing Bivens claims, since the Act takes away the main alternative remedial scheme that previously existed. Indeed, an (incorrect) interpretation of the Westfall Act as preempting non-federal remedies but not authorizing equivalent federal remedies may well raise significant constitutional questions--questions that have thus far been dramatically under-appreciated by the lower courts, but that must be taken seriously going forward. And if courts conclude that, in appropriate cases, the question really should be Bivens or nothing, they must recognize that either answer requires judicial lawmaking--and not just recognition of a federal cause of action

X-ray emission from an FU Ori star in early outburst: HBC 722

Aims: We conducted the first X-ray observations of the newly erupting FU Ori-type outburst in HBC 722 (V2493 Cyg) with the aim to characterize its X-ray behavior and near-stellar environment during early outburst. Methods: We used data from the XMM-Newton and Chandra X-ray observatories to measure X-ray source temperatures and luminosities as well as the gas column densities along the line of sight toward the source. Results: We report a Chandra X-ray detection of HBC 722 with an X-ray luminosity of LX ~ 4E30 erg s-1. The gas column density exceeds values expected from optical extinction and standard gas-to-dust ratios. We conclude that dust-free gas masses are present around the star, such as strong winds launched from the inner disk, or massive accretion columns. A tentative detection obtained by XMM-Newton two years earlier after an initial optical peak revealed a fainter X-ray source with only weak absorption.Comment: Accepted for Astronomy & Astrophysics Letters on September 17, 201

Can retinal ganglion cell dipoles seed iso-orientation domains in the visual cortex?

It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC mosaics. While this Moir\'{e}-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.Comment: 9 figures + 1 Supplementary figure and 1 Supplementary tabl

On 3-dimensional lattice walks confined to the positive octant

Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in $\{0, \pm 1\}^2$: the generating function is D-finite if and only if a certain group associated with the step set is finite. We explore in this paper the analogous problem for 3-dimensional walks confined to the positive octant. The first difficulty is their number: there are 11074225 non-trivial and non-equivalent step sets in $\{0, \pm 1\}^3$ (instead of 79 in the quadrant case). We focus on the 35548 that have at most six steps. We apply to them a combined approach, first experimental and then rigorous. On the experimental side, we try to guess differential equations. We also try to determine if the associated group is finite. The largest finite groups that we find have order 48 -- the larger ones have order at least 200 and we believe them to be infinite. No differential equation has been detected in those cases. On the rigorous side, we apply three main techniques to prove D-finiteness. The algebraic kernel method, applied earlier to quadrant walks, works in many cases. Certain, more challenging, cases turn out to have a special Hadamard structure, which allows us to solve them via a reduction to problems of smaller dimension. Finally, for two special cases, we had to resort to computer algebra proofs. We prove with these techniques all the guessed differential equations. This leaves us with exactly 19 very intriguing step sets for which the group is finite, but the nature of the generating function still unclear.Comment: Final version, to appear in Annals of Combinatorics. 36 page