Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

Quantum State During and after O(4)O(4)-Symmetric Bubble Nucleation with Gravitaional Effects

We extend our previous analysis of the quantum state during and after $O(4)$-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without gravitational effects. In a special case of a conformally coupled scalar field which is massless except on the bubble wall, the state is found to be conformally equivalent to the case without gravity.Comment: 31 pages plain Tex file, uuencoded postscript figure file is available from [email protected] upon request, KUNS126

Relaxation and Metastability in the RandomWalkSAT search procedure

An analysis of the average properties of a local search resolution procedure for the satisfaction of random Boolean constraints is presented. Depending on the ratio alpha of constraints per variable, resolution takes a time T_res growing linearly (T_res \sim tau(alpha) N, alpha < alpha_d) or exponentially (T_res \sim exp(N zeta(alpha)), alpha > alpha_d) with the size N of the instance. The relaxation time tau(alpha) in the linear phase is calculated through a systematic expansion scheme based on a quantum formulation of the evolution operator. For alpha > alpha_d, the system is trapped in some metastable state, and resolution occurs from escape from this state through crossing of a large barrier. An annealed calculation of the height zeta(alpha) of this barrier is proposed. The polynomial/exponentiel cross-over alpha_d is not related to the onset of clustering among solutions.Comment: 23 pages, 11 figures. A mistake in sec. IV.B has been correcte

Terrestrial Implications of Cosmological Gamma-Ray Burst Models

The observation by the BATSE instrument on the Compton Gamma Ray Observatory that gamma-ray bursts (GRBs) are distributed isotropically around the Earth but nonuniformly in distance has led to the widespread conclusion that GRBs are most likely to be at cosmological distances, making them the most luminous sources known in the Universe. If bursts arise from events that occur in normal galaxies, such as neutron star binary inspirals, then they will also occur in our Galaxy about every hundred thousand to million years. The gamma-ray flux at the Earth due to a Galactic GRB would far exceed that from even the largest solar flares. The absorption of this radiation in the atmosphere would substantially increase the stratospheric nitric oxide concentration through photodissociation of N$_2$, greatly reducing the ozone concentration for several years through NO$_x$ catalysis, with important biospheric effects due to increased solar ultraviolet flux. A nearby GRB may also leave traces in anomalous radionuclide abundances.Comment: uuencoded, gzip-ed postscript; 6 pages; submitted to ApJ Letter

An EPTAS for scheduling jobs on uniform processors using an MILP relaxation with a constant number of integral variables

We present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of (n/\epsilon)^{O(1/\epsilon^2)}. Our algorithm, based on a new mixed integer linear programming (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error $\epsilon$ of the optimum, and has running time 2^{O(1/\epsilon^2 \log(1/\epsilon)^3)} + poly(n)

Citraconate inhibits ACOD1 (IRG1) catalysis, reduces interferon responses and oxidative stress, and modulates inflammation and cell metabolism

Although the immunomodulatory and cytoprotective properties of itaconate have been studied extensively, it is not known whether its naturally occurring isomers mesaconate and citraconate have similar properties. Here, we show that itaconate is partially converted to mesaconate intracellularly and that mesaconate accumulation in macrophage activation depends on prior itaconate synthesis. When added to human cells in supraphysiological concentrations, all three isomers reduce lactate levels, whereas itaconate is the strongest succinate dehydrogenase (SDH) inhibitor. In cells infected with influenza A virus (IAV), all three isomers profoundly alter amino acid metabolism, modulate cytokine/chemokine release and reduce interferon signalling, oxidative stress and the release of viral particles. Of the three isomers, citraconate is the strongest electrophile and nuclear factor-erythroid 2-related factor 2 (NRF2) agonist. Only citraconate inhibits catalysis of itaconate by cis-aconitate decarboxylase (ACOD1), probably by competitive binding to the substrate-binding site. These results reveal mesaconate and citraconate as immunomodulatory, anti-oxidative and antiviral compounds, and citraconate as the first naturally occurring ACOD1 inhibitor

An ancestry informative marker set for determining continental origin: validation and extension using human genome diversity panels

<p>Abstract</p> <p>Background</p> <p>Case-control genetic studies of complex human diseases can be confounded by population stratification. This issue can be addressed using panels of ancestry informative markers (AIMs) that can provide substantial population substructure information. Previously, we described a panel of 128 SNP AIMs that were designed as a tool for ascertaining the origins of subjects from Europe, Sub-Saharan Africa, Americas, and East Asia.</p> <p>Results</p> <p>In this study, genotypes from Human Genome Diversity Panel populations were used to further evaluate a 93 SNP AIM panel, a subset of the 128 AIMS set, for distinguishing continental origins. Using both model-based and relatively model-independent methods, we here confirm the ability of this AIM set to distinguish diverse population groups that were not previously evaluated. This study included multiple population groups from Oceana, South Asia, East Asia, Sub-Saharan Africa, North and South America, and Europe. In addition, the 93 AIM set provides population substructure information that can, for example, distinguish Arab and Ashkenazi from Northern European population groups and Pygmy from other Sub-Saharan African population groups.</p> <p>Conclusion</p> <p>These data provide additional support for using the 93 AIM set to efficiently identify continental subject groups for genetic studies, to identify study population outliers, and to control for admixture in association studies.</p

Citraconate inhibits ACOD1 (IRG1) catalysis, reduces interferon responses and oxidative stress, and modulates inflammation and cell metabolism

Although the immunomodulatory and cytoprotective properties of itaconate have been studied extensively, it is not known whether its naturally occurring isomers mesaconate and citraconate have similar properties. Here, we show that itaconate is partially converted to mesaconate intracellularly and that mesaconate accumulation in macrophage activation depends on prior itaconate synthesis. When added to human cells in supraphysiological concentrations, all three isomers reduce lactate levels, whereas itaconate is the strongest succinate dehydrogenase (SDH) inhibitor. In cells infected with influenza A virus (IAV), all three isomers profoundly alter amino acid metabolism, modulate cytokine/chemokine release and reduce interferon signalling, oxidative stress and the release of viral particles. Of the three isomers, citraconate is the strongest electrophile and nuclear factor-erythroid 2-related factor 2 (NRF2) agonist. Only citraconate inhibits catalysis of itaconate by cis-aconitate decarboxylase (ACOD1), probably by competitive binding to the substrate-binding site. These results reveal mesaconate and citraconate as immunomodulatory, anti-oxidative and antiviral compounds, and citraconate as the first naturally occurring ACOD1 inhibitor. [Image: see text