Exponential Time Complexity of Weighted Counting of Independent Sets

We consider weighted counting of independent sets using a rational weight x: Given a graph with n vertices, count its independent sets such that each set of size k contributes x^k. This is equivalent to computation of the partition function of the lattice gas with hard-core self-repulsion and hard-core pair interaction. We show the following conditional lower bounds: If counting the satisfying assignments of a 3-CNF formula in n variables (#3SAT) needs time 2^{\Omega(n)} (i.e. there is a c>0 such that no algorithm can solve #3SAT in time 2^{cn}), counting the independent sets of size n/3 of an n-vertex graph needs time 2^{\Omega(n)} and weighted counting of independent sets needs time 2^{\Omega(n/log^3 n)} for all rational weights x\neq 0. We have two technical ingredients: The first is a reduction from 3SAT to independent sets that preserves the number of solutions and increases the instance size only by a constant factor. Second, we devise a combination of vertex cloning and path addition. This graph transformation allows us to adapt a recent technique by Dell, Husfeldt, and Wahlen which enables interpolation by a family of reductions, each of which increases the instance size only polylogarithmically.Comment: Introduction revised, differences between versions of counting independent sets stated more precisely, minor improvements. 14 page

Psychosocial Health Disparities Among Black Bisexual Men in the U.S.: Effects of Sexuality Nondisclosure and Gay Community Support

Compared with Black gay men, Black bisexual men experience psychosocial health disparities, including depression, polydrug use, physical assault, and intimate partner violence (IPV). Black bisexual men are also less likely to disclose their sexuality, which may result in them receiving less sexual minority community support, exacerbating psychosocial health disparities. We assessed relationships between bisexual behavior, bisexual identity, sexuality nondisclosure, gay community support, and psychosocial morbidities among Black men who have sex with men (MSM). Between 2014 and 2017, survey data were collected from Black MSM ≥ 18 years old (n = 4430) at Black Pride events in six U.S. cities. We differentiated between bisexual-identified men reporting past-year sex with men and women (bisexual MSMW, 8.4%); gay-identified men reporting sex with men only (gay MSMO, 73.1%); gay MSMW (8.0%); and bisexual MSMO (8.4%). Multivariable regressions contrasted these groups by psychosocial morbidities, sexuality nondisclosure, and gay community support. Structural equation models assessed total, direct, and indirect effects. Compared with gay MSMO, bisexual MSMW and gay MSMW were significantly more likely to report polydrug use, depression symptoms, IPV, physical assault, sexuality nondisclosure, and lack of gay community support. Lack of gay community support had significant indirect effects on the relationships between bisexual behavior and psychosocial morbidity (p < .001) and between bisexual identity and psychosocial morbidity (p < .001). Sexuality nondisclosure had significant indirect effects on relationships between bisexual behavior (p < .001), bisexual identity (p < .001), and lack of gay community support. Psychosocial health disparities experienced by Black bisexual men are associated with both bisexual behavior and bisexual identity. Interventions decreasing biphobia will facilitate opportunities for protective sexuality disclosure and access to sexual minority community support

Gait Characteristics and Cognitive Function in Middle-Aged Adults With and Without Type 2 Diabetes Mellitus: Data from ENBIND

Type 2 Diabetes Mellitus (T2DM) in midlife is associated with a greater risk of dementia in later life. Both gait speed and spatiotemporal gait characteristics have been associated with later cognitive decline in community-dwelling older adults. Thus, the assessment of gait characteristics in uncomplicated midlife T2DM may be important in selecting-out those with T2DM at greatest risk of later cognitive decline. We assessed the relationship between Inertial Motion Unit (IMUs)- derived gait characteristics and cognitive function assessed via Montreal Cognitive Assessment (MOCA)/detailed neuropsychological assessment battery (CANTAB) in middle-aged adults with and without uncomplicated T2DM using both multivariate linear regression and a neural network approach. Gait was assessed under (i) normal walking, (ii) fast (maximal) walking and (iii) cognitive dual-task walking (reciting alternate letters of the alphabet) conditions. Overall, 138 individuals were recruited (n = 94 with T2DM; 53% female, 52.8 8.3 years; n = 44 healthy controls, 43% female, 51.9 8.1 years). Midlife T2DM was associated with significantly slower gait velocity on both slow and fast walks (both p \u3c 0.01) in addition to a longer stride time and greater gait complexity during normal walk (both p \u3c 0.05). Findings persisted following covariate adjustment. In analyzing cognitive performance, the strongest association was observed between gait velocity and global cognitive function (MOCA). Significant associations were also observed between immediate/delayed memory performance and gait velocity. Analysis using a neural network approach did not outperform multivariate linear regression in predicting cognitive function (MOCA) from gait velocity. Our study demonstrates the impact of uncomplicated T2DM on gait speed and gait characteristics in midlife, in addition to the striking relationship between gait characteristics and global cognitive function/memory performance in midlife. Further studies are needed to evaluate the longitudinal relationship between midlife gait characteristics and later cognitive decline, which may aid in selecting-out those with T2DM at greatest-risk for preventative interventions

Virus infection and grazing exert counteracting influences on survivorship of native bunchgrass seedlings competing with invasive exotics

1.  Invasive annual grasses introduced by European settlers have largely displaced native grassland vegetation in California and now form dense stands that constrain the establishment of native perennial bunchgrass seedlings. Bunchgrass seedlings face additional pressures from both livestock grazing and barley and cereal yellow dwarf viruses (B/CYDVs), which infect both young and established grasses throughout the state. 2.  Previous work suggested that B/CYDVs could mediate apparent competition between invasive exotic grasses and native bunchgrasses in California. 3.  To investigate the potential significance of virus-mediated mortality for early survivorship of bunchgrass seedlings, we compared the separate and combined effects of virus infection, competition and simulated grazing in a field experiment. We infected two species of young bunchgrasses that show different sensitivity to B/CYDV infection, subjected them to competition with three different densities of exotic annuals crossed with two clipping treatments, and monitored their growth and first-year survivorship. 4.  Although virus infection alone did not reduce first-year survivorship, it halved the survivorship of bunchgrasses competing with exotics. Within an environment in which competition strongly reduces seedling survivorship (as in natural grasslands), virus infection therefore has the power to cause additional seedling mortality and alter patterns of establishment. 5.  Surprisingly, clipping did not reduce bunchgrass survivorship further, but rather doubled it and disproportionately increased survivorship of infected bunchgrasses. 6.  Together with previous work, these findings show that B/CYDVs can be potentially powerful elements influencing species interactions in natural grasslands. 7.  More generally, our findings demonstrate the potential significance of multitrophic interactions in virus ecology. Although sometimes treated collectively as plant ‘predators’, viruses and herbivores may exert influences that are distinctly different, even counteracting

The complexity of the Pk partition problem and related problems in bipartite graphs

International audienceIn this paper, we continue the investigation made in [MT05] about the approximability of Pk partition problems, but focusing here on their complexity. Precisely, we aim at designing the frontier between polynomial and NP-complete versions of the Pk partition problem in bipartite graphs, according to both the constant k and the maximum degree of the input graph. We actually extend the obtained results to more general classes of problems, namely, the minimum k-path partition problem and the maximum Pk packing problem. Moreover, we propose some simple approximation algorithms for those problems

Human resource management as a profession in South Africa

Orientation: Various countries recognise human resource (HR) management as a bona fide profession. Research purpose: The objective of this study was to establish whether one could regard HR management, as practised in South Africa, as a profession. Motivation for the study: Many countries are reviewing the professionalisation of HR management. Therefore, it is necessary to establish the professional standing of HR management in South Africa. Research design, approach and method: The researchers used a purposive sampling strategy involving 95 participants. The researchers achieved triangulation by analysing original documents of the regulating bodies of the medical, legal, engineering and accounting professions internationally and locally as well as the regulating bodies of HR management in the United Kingdom (UK), the United States of America (USA) and Canada. Seventy- eight HR professionals registered with the South African Board for People Practices (SABPP) completed a questionnaire. The researchers analysed the data using content analysis and Lawshe’s Content Validity Ratio (CVR). Main findings: The results confirm that HR management in South Africa adheres to the four main pillars of professionalism and is a bona fide profession. Practical/managerial implications: The article highlights the need to regulate and formalise HR management in South Africa. Contribution/value-add: This study identifies a number of aspects that determine professionalism and isolates the most important elements that one needs to consider when regulating the HR profession

An eclipsing 47 minute double white dwarf binary at 400 pc

We present the discovery of the eclipsing double white dwarf (WD) binary WDJ 022558.21−692025.38 that has an orbital period of 47.19 min. Following identification with the Transiting Exoplanet Survey Satellite, we obtained time-series ground based spectroscopy and high-speed multi-band ULTRACAM photometry which indicate a primary DA WD of mass 0.40 ± 0.04 M⊙ and a 0.28 ± 0.02 M⊙ mass secondary WD, which is likely of type DA as well. The system becomes the third-closest eclipsing double WD binary discovered with a distance of approximately 400 pc and will be a detectable source for upcoming gravitational wave detectors in the mHz frequency range. Its orbital decay will be measurable photometrically within 10 yrs to a precision of better than 1%. The fate of the binary is to merge in approximately 41 Myr, likely forming a single, more massive WD

TIC 378898110: A bright, short-period AM CVn binary in TESS

AM CVn-type systems are ultracompact, helium-accreting binary systems which are evolutionarily linked to the progenitors of thermonuclear supernovae and are expected to be strong Galactic sources of gravitational waves detectable to upcoming space-based interferometers. AM CVn binaries with orbital periods ≲ 20–23 min exist in a constant high state with a permanently ionised accretion disc. We present the discovery of TIC 378898110, a bright (G = 14.3 mag), nearby (309.3 ± 1.8 pc), high-state AM CVn binary discovered in TESS two-minute-cadence photometry. At optical wavelengths this is the third-brightest AM CVn binary known. The photometry of the system shows a 23.07172(6) min periodicity, which is likely to be the ‘superhump’ period and implies an orbital period in the range 22–23 min. There is no detectable spectroscopic variability. The system underwent an unusual, year-long brightening event during which the dominant photometric period changed to a shorter period (constrained to 20.5 ± 2.0 min), which we suggest may be evidence for the onset of disc-edge eclipses. The estimated mass transfer rate, log(M˙ /M⊙yr−1 ) = −6.8±1.0, is unusually high and may suggest a high-mass or thermally inflated donor. The binary is detected as an X-ray source, with a flux of 9.2+4.2 −1.8 ×10−13 erg cm−2s−1 in the 0.3–10 keV range. TIC 378898110 is the shortest-period binary system discovered with TESS, and its large predicted gravitational-wave amplitude makes it a compelling verification binary for future space-based gravitational wave detectors