Excluding a ladder

A ladder is a $2 \times k$ grid graph. When does a graph class $\mathcal{C}$ exclude some ladder as a minor? We show that this is the case if and only if all graphs $G$ in $\mathcal{C}$ admit a proper vertex coloring with a bounded number of colors such that for every $2$-connected subgraph $H$ of $G$, there is a color that appears exactly once in $H$. This type of vertex coloring is a relaxation of the notion of centered coloring, where for every connected subgraph $H$ of $G$, there must be a color that appears exactly once in $H$. The minimum number of colors in a centered coloring of $G$ is the treedepth of $G$, and it is known that classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor. In this sense, the structure of graphs excluding a fixed ladder as a minor resembles the structure of graphs without long paths. Another similarity is as follows: It is an easy observation that every connected graph with two vertex-disjoint paths of length $k$ has a path of length $k+1$. We show that every $3$-connected graph which contains as a minor a union of sufficiently many vertex-disjoint copies of a $2 \times k$ grid has a $2 \times (k+1)$ grid minor. Our structural results have applications to poset dimension. We show that posets whose cover graphs exclude a fixed ladder as a minor have bounded dimension. This is a new step towards the goal of understanding which graphs are unavoidable as minors in cover graphs of posets with large dimension.Comment: v3: revised according to referees' comment

A new measurement of the Hubble constant and matter content of the Universe using extragalactic background light γ\gamma-ray attenuation

The Hubble constant $H_{0}$ and matter density $\Omega_{m}$ of the Universe are measured using the latest $\gamma$-ray attenuation results from Fermi-LAT and Cherenkov telescopes. This methodology is based upon the fact that the extragalactic background light supplies opacity for very high energy photons via photon-photon interaction. The amount of $\gamma$-ray attenuation along the line of sight depends on the expansion rate and matter content of the Universe. This novel strategy results in a value of $H_{0}=67.4_{-6.2}^{+6.0}$~km~s$^{-1}$~Mpc$^{-1}$ and $\Omega_{m}=0.14_{-0.07}^{+0.06}$. These estimates are independent and complementary to those based on the distance ladder, cosmic microwave background (CMB), clustering with weak lensing, and strong lensing data. We also produce a joint likelihood analysis of our results from $\gamma$ rays and these from more mature methodologies, excluding the CMB, yielding a combined value of $H_{0}=66.6\pm 1.6$~km~s$^{-1}$~Mpc$^{-1}$ and $\Omega_{m}=0.29\pm 0.02$.Comment: 9 pages, 6 figures, 1 table. Accepted by Ap

Transformations to achieve the Sustainable Development Goals Includes the SDG Index and Dashboards. Sustainable Development Report 2019

The Sustainable Development Report 2019 presents an updated SDG Index and Dashboards with a refined assessment of countries’ distance to SDG targets. The report has been successfully audited for the first time by the European Commission Joint Research Centre. New indicators have been included, primarily to refine the indicator selection on agriculture, diets, gender equality and freedom of speech. We have also added more metrics for international spillovers, including on fatal work accidents. A new website and data visualization tools are available (http://sustainabledevelopment.report). Once again, Nordic countries – Denmark, Sweden and Finland – top the SDG Index. Yet, even these countries face major challenges in implementing one or several SDGs. No country is on track for achieving all 17 goals with major performance gaps even in the top countries on SDG 12 (Responsible Consumption and Production), SDG 13 (Climate Action), SDG 14 (Life Below Water) and SDG 15 (Life on Land). Income and wealth inequalities, as well as gaps in health and education outcomes by population groups also remain important policy challenges in developing and developed countries alike. The Sustainable Development Report 2019 generates seven major findings: 1. High-level political commitment to the SDGs is falling short of historic promises In September 2019, heads-of-states and governments will convene for the first time in person at the UN in New York to review progress on their promises made four years after the adoption of the 2030 Agenda. Yet, our in-depth analyses show that many have not taken the critical steps to implement the SDGs. Out of 43 countries surveyed on SDG implementation efforts, including all G20 countries and countries with a population greater than 100 million, 33 countries have endorsed the SDGs in official statements since January 1st, 2018. Yet in only 18 of them do central budget documents mention the SDGs. This gap between rhetoric and action must be closed. 2. The SDGs can be operationalized through six SDG Transformations SDG implementation can be organized along the following Transformations: 1. Education, Gender, and Inequality; 2. Health, Wellbeing, and Demography; 3. Energy Decarbonization and Sustainable Industry; 4. Sustainable Food, Land, Water, Oceans; 5. Sustainable Cities and Communities; and 6. Digital Revolution for Sustainable Development. The transformations respect strong interdependencies across the SDGs and can be operationalized by well-defined parts of governments in collaboration with civil society, business, and other stakeholders. They must be underpinned and guided by the principles of Leave No One Behind and Circularity and Decoupling of resource use from human wellbeing. 3. Trends on climate (SDG 13) and biodiversity (SDG 14 and SDG 15) are alarming On average, countries obtain their worst scores on SDG 13 (Climate Action), SDG 14 (Life Below Water) and SDG 15 (Life on Land). No country obtains a “green rating” (synonym of SDG achieved) on SDG 14 (Life Below Water). Trends on greenhouse gas emissions and, even more so, on threatened species are moving in the wrong direction. These findings are in line with the recent reports from the IPCC and IPBES on climate change mitigation and biodiversity protection, respectively. 4. Sustainable land-use and healthy diets require integrated agriculture, climate and health policy interventions Land use and food production are not meeting people’s needs. Agriculture destroys forests and biodiversity, squanders water and releases one-quarter of global greenhouse-gas emissions. In total, 78% of world nations for which data are available obtain a “red rating” (synonym of major SDG challenge) on sustainable nitrogen management; the highest number of “red” rating across all indicators included in the report. At the same time, one-third of food is wasted, 800 million people remain undernourished, 2 billion are deficient in micronutrients, and obesity is on the rise. New indicators on nations’ trophic level and yield gap closure highlight the depth of the challenge. Transformations towards sustainable landuse and food systems are required to balance efficient and resilient agriculture and forestry with biodiversity conservation and restoration as well as healthy diets

Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

We calculate the Landau interaction function f(k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.Comment: 10 pages, 16 figure

Absence of extended states in a ladder model of DNA

We consider a ladder model of DNA for describing carrier transport in a fully coherent regime through finite segments. A single orbital is associated to each base, and both interstrand and intrastrand overlaps are considered within the nearest-neighbor approximation. Conduction through the sugar-phosphate backbone is neglected. We study analytically and numerically the spatial extend of the corresponding states by means of the Landauer and Lyapunov exponents. We conclude that intrinsic-DNA correlations, arising from the natural base pairing, does not suffice to observe extended states, in contrast to previous claims.Comment: 4 RevTex pages, 4 figures include

Improving entanglement and thermodynamic R\'enyi entropy measurements in quantum Monte Carlo

We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved estimators for the latter allows to obtain very good estimates for entanglement R\'enyi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated providing access to the thermodynamic R\'enyi entropies with high accuracy. We also explore a recently-proposed method for the reconstruction of the entanglement spectrum from entanglement R\'enyi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal R\'enyi entropies.Comment: 15 pages, 11 figure

Rapid Detection of Avian Eimeria Species Using Denaturing Gradient Gel Electrophoresis

A denaturing gradient gel electrophoresis (DGGE) assay was developed to rapidly discriminate species of avian Eimeria. Amplification by PCR of the small subunit ribosomal RNA gene (approximately 1,600 nucleotides) with Eimeria genus-specific primers followed by cloning and sequencing allowed us to carry out phylogenetic analyses and identify clone sequences to species level in most cases. Clones were subsequently used to amplify a smaller fragment (approximately 120 nucleotides) suitable for DGGE. The fragments were separated on denaturing gradient gel and bands with unique migration distances were mixed to obtain an identification ladder. The identification ladder and PCR products obtained from DNA extracted from fecal samples from several poultry farms were compared. Applying the DGGE method in this study allowed a rapid differentiation of Eimeria species present in fecal samples collected from poultry farms

Phase diagrams of spin ladders with ferromagnetic legs

The low-temperature properties of the spin S=1/2 ladder with anisotropic ferromagnetic legs are studied using the continuum limit bosonization approach. The weak-coupling ground state phase diagram of the model is obtained for a wide range of coupling constants and several unconventional gapless ''spin-liquid'' phases are shown to exist for ferromagnetic coupling. The behavior of the ladder system in the vicinity of the ferromagnetic instability point is discussed in detail.Comment: 11 pages, 4 figure