When Gravity Fails: Local Search Topology

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the time spent in local search. We analyze and characterize plateaus for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e., global minima) of randomly generated problem instances form clusters, which behave similarly to local minima. We revisit several enhancements of local search algorithms and explain their performance in light of our results. Finally we discuss strategies for creating the next generation of local search algorithms.Comment: See http://www.jair.org/ for any accompanying file

An updated assessment of past and future warming over France based on a regional observational constraint

Building on CMIP6 climate simulations, updated global and regional observations, and recently introduced statistical methods, we provide an updated assessment of past and future warming over France. Following the IPCC AR6 and recent global-scale studies, we combine model results with observations to constrain climate change at the regional scale. Over mainland France, the forced warming in 2020 with respect to 1900–1930 is assessed to be 1.66 [1.41 to 1.90] ∘C, i.e., in the upper range of the CMIP6 estimates, and is almost entirely human-induced. A refined view of the seasonality of this past warming is provided through updated daily climate normals. Projected warming in response to an intermediate emission scenario is assessed to be 3.8 ∘C (2.9 to 4.8 ∘C) in 2100 and rises up to 6.7 [5.2 to 8.2] ∘C in a very high emission scenario, i.e., substantially higher than in previous ensembles of global and regional simulations. Winter warming and summer warming are expected to be about 15 % lower than and 30 % higher than the annual mean warming, respectively, for all scenarios and time periods. This work highlights the importance of combining various lines of evidence, including model and observed data, to deliver the most reliable climate information. This refined regional assessment can feed adaptation planning for a range of activities and provides additional rationale for urgent climate action. Code is made available to facilitate replication over other areas or political entities.</p

A Halo Model with Environment Dependence: Theoretical Considerations

We present a modification of the standard halo model with the goal of providing an improved description of galaxy clustering. Recent surveys, like the Sloan Digital Sky Survey (SDSS) and the Anglo-Australian Two-degree survey (2dF), have shown that there seems to be a correlation between the clustering of galaxies and their properties such as metallicity and star formation rate, which are believed to be environment-dependent. This environmental dependence is not included in the standard halo model where the host halo mass is the only variable specifying galaxy properties. In our approach, the halo properties i.e., the concentration, and the Halo Occupation Distribution --HOD-- prescription, will not only depend on the halo mass (like in the standard halo model) but also on the halo environment. We examine how different environmental dependence of halo concentration and HOD prescription affect the correlation function. We see that at the level of dark matter, the concentration of haloes affects moderately the dark matter correlation function only at small scales. However the galaxy correlation function is extremely sensitive to the HOD details, even when only the HOD of a small fraction of haloes is modified.Comment: 23 pages, 17 figures. Accepted for publication in MNRA

Physical properties underlying observed kinematics of satellite galaxies

We study the kinematics of satellites around isolated galaxies selected from the Sloan Digital Sky Survey (SDSS) spectroscopic catalog. Using a model of the phase-space density previously measured for the halos of LCDM dark matter cosmological simulations, we determine the properties of the halo mass distribution and the orbital anisotropy of the satellites as a function of the colour-based morphological type and the stellar mass of the central host galaxy. We place constraints on the halo mass and the concentration parameter of dark matter and the satellite number density profiles. We obtain a concentration-mass relation for galactic dark matter haloes that is consistent with predictions of a standard LCDM cosmological model. At given halo or stellar mass, red galaxies have more concentrated halos than their blue counterparts. The fraction of dark matter within a few effective radii is minimal for 11.25<log M_star<11.5. The number density profile of the satellites appears to be shallower than of dark matter, with the scale radius typically 60 per cent larger than of dark matter. The orbital anisotropy around red hosts exhibits a mild excess of radial motions, in agreement with the typical anisotropy profiles found in cosmological simulations, whereas blue galaxies are found to be consistent with an isotropic velocity distribution. Our new constraints on the halo masses of galaxies are used to provide analytic approximations of the halo-to-stellar mass relation for red and blue galaxies.Comment: 12 pages, 11 figures; accepted for publication in MNRAS (updated references

Future global climate: scenario-based projections and near-term information

This chapter assesses simulations of future global climate change, spanning time horizons from the near term (2021–2040), mid-term (2041–2060), and long term (2081–2100) out to the year 2300. Changes are assessed relative to both the recent past (1995–2014) and the 1850–1900 approximation to the pre-industrial period

On the van der Waerden numbers w(2;3,t)

We present results and conjectures on the van der Waerden numbers w(2;3,t) and on the new palindromic van der Waerden numbers pdw(2;3,t). We have computed the new number w(2;3,19) = 349, and we provide lower bounds for 20 <= t <= 39, where for t <= 30 we conjecture these lower bounds to be exact. The lower bounds for 24 <= t <= 30 refute the conjecture that w(2;3,t) <= t^2, and we present an improved conjecture. We also investigate regularities in the good partitions (certificates) to better understand the lower bounds. Motivated by such reglarities, we introduce *palindromic van der Waerden numbers* pdw(k; t_0,...,t_{k-1}), defined as ordinary van der Waerden numbers w(k; t_0,...,t_{k-1}), however only allowing palindromic solutions (good partitions), defined as reading the same from both ends. Different from the situation for ordinary van der Waerden numbers, these "numbers" need actually to be pairs of numbers. We compute pdw(2;3,t) for 3 <= t <= 27, and we provide lower bounds, which we conjecture to be exact, for t <= 35. All computations are based on SAT solving, and we discuss the various relations between SAT solving and Ramsey theory. Especially we introduce a novel (open-source) SAT solver, the tawSolver, which performs best on the SAT instances studied here, and which is actually the original DLL-solver, but with an efficient implementation and a modern heuristic typical for look-ahead solvers (applying the theory developed in the SAT handbook article of the second author).Comment: Second version 25 pages, updates of numerical data, improved formulations, and extended discussions on SAT. Third version 42 pages, with SAT solver data (especially for new SAT solver) and improved representation. Fourth version 47 pages, with updates and added explanation