The Satisfiability Threshold for a Seemingly Intractable Random Constraint Satisfaction Problem

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability threshold, and for which random instances with density near that threshold appear to be computationally difficult. More formally, it is the first random CSP model for which the satisfiability threshold is known and which shares the following characteristics with random k-SAT for k >= 3. The problem is NP-complete, the satisfiability threshold occurs when there is a linear number of clauses, and a uniformly random instance with a linear number of clauses asymptotically almost surely has exponential resolution complexity.Comment: This is the long version of a paper that will be published in the SIAM Journal on Discrete Mathematics. This long version includes an appendix and a computer program. The contents of the paper are unchanged in the latest version. The format of the arxiv submission was changed so that the computer program will appear as an ancillary file. Some comments in the computer program were update

Placing problems from phylogenetics and (quantified) propositional logic in the polynomial hierarchy

In this thesis, we consider the complexity of decision problems from two different areas of research and place them in the polynomial hierarchy: phylogenetics and (quantified) propositional logic. In phylogenetics, researchers study the evolutionary relationships between species. The evolution of a particular gene can often be represented by a single phylogenetic tree. However, in order to model non-tree-like events on a species level such as hybridization and lateral gene transfer, phylogenetic networks are used. They can be considered as a structure that embeds a whole set of phylogenetic trees which is called the display set of the network. There are many interesting questions revolving around display sets and one is often interested in the computational complexity of the considered problems for particular classes of networks. In this thesis, we present our results for different questions related to the display sets of two networks and place the corresponding decision problems in the polynomial hierarchy. Another interesting question concerns the reconstruction of networks: given a set T of phylogenetic trees, can we construct a phylogenetic network with certain properties that embeds all trees in T? For a class of networks that satisfies certain temporal properties, Humphries et al. (2013) established a characterization for when this is possible based on the existence of a particular structure for T, a so-called cherry-picking sequence. We obtain several complexity results for the existence of such a sequence: Deciding the existence of a cherry-picking sequence turns out to be NP-complete for each non-trivial number (i.e., at least two) of given trees. Thereby, we settle the open question stated by Humphries et al. (2013) on the complexity for the case |T| = 2. On the positive side, we identify a special case that we place in the complexity class P by exploring connections to automata theory. Regarding propositional logic, we present our complexity results for the classical satisfiability problem (and variants resp. quantified generalizations thereof) and place the considered variants in the polynomial hierarchy. A common theme is to consider bounded variable appearances in combination with other restrictions such as monotonicity of the clauses or planarity of the incidence graph. This research was inspired by the conjecture that Monotone 3-SAT remains NP-complete if each variable appears at most five times which was stated in the scribe notes of a lecture held by Erik Demaine; we confirm this conjecture in an even more restricted setting where each variable appears exactly four times

Iberian peninsula ecosystem carbon fluxes: a model-data integration study

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia do Ambiente pela Universidade Nova de Lisboa,Faculdade de Ciências e TecnologiaTerrestrial ecosystems play a key role within the context of the global carbon cycle. Characterizing and understanding ecosystem level responses and feedbacks to climate drivers is essential for diagnostic purposes as well as climate modelling projections. Consequently,numerous modelling and data driven approaches emerge, aiming the appraisal of biosphereatmosphere carbon fluxes. The combination of biogeochemical models with observations of ecosystem carbon fluxes in a model-data integration framework enables the recognition of potential limitations of modelling approaches. In this regard, the steady-state assumption represents a general approach in the initialization routines of biogeochemical models that entails limitations in the ability to simulate net ecosystem fluxes and in model development exercises. The present research addresses the generalized assumption of initial steady-state conditions in ecosystem carbon pools for modelling carbon fluxes of terrestrial ecosystems, from local to regional scales. At local scale, this study aims to evaluate the implications of equilibrium assumptions on modelling performance and on optimized parameters and uncertainty estimates based on a model-data integration approach. These results further aim to support the estimates of regional net ecosystem fluxes, following a bottom-up approach, by focusing on parameters governing net primary production (NPP) and heterotrophic respiration (RH)processes, which determine the simulation of the net ecosystem production fluxes in the CASA model. An underlying goal of the current research is addressed by focusing on Mediterranean ecosystem types, or ecosystems potentially present in Iberia, and evaluate the general ability of terrestrial biogeochemical models in estimating net ecosystem fluxes for the Iberian Peninsula region. At regional scales, and given the limited information available, the main objective is to minimize the implications of the initial conditions in the evaluation of the temporal dynamics of net ecosystem fluxes. Inverse model parameter optimizations at site level are constrained by eddy-covariance measurements of net ecosystem fluxes and driven by local observations of meteorological variables and vegetation biophysical variables from remote sensing products. Optimizations under steady-state conditions show significantly poorer model performance and higher parameter uncertainties when compared to optimizations under relaxed initial conditions. In addition, assuming initial steady-state conditions tend to bias parameter retrievals – reducing NPP sensitivity to water availability and RH responses to temperature – in order to prescribe sink conditions. But nonequilibrium conditions can be experienced in soil and/or vegetation carbon pools under alternative underlying dynamics, which are solely discernible through the integration of additional information sources, circumventing equifinality issues.Portuguese Foundation for Science and Technology (FCT),the European Union under Operational Program “Science and Innovation” (POCI 2010), PhD grant ref. SFRH/BD/6517/2001, co-sponsored by the European Social Fund. Further support,concerning the final months of the PhD, was provided by a Max Planck Society research fellowship

Counting Solutions to Random CNF Formulas

We give the first efficient algorithm to approximately count the number of solutions in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previous counting algorithm was due to Montanari and Shah and was based on the correlation decay method, which works up to densities $(1+o_k(1))\frac{2\log k}{k}$, the Gibbs uniqueness threshold for the model. Instead, our algorithm harnesses a recent technique by Moitra to work for random formulas. The main challenge in our setting is to account for the presence of high-degree variables whose marginal distributions are hard to control and which cause significant correlations within the formula

Touts and Despots

Diese Dissertation folgt Fernando Pó Arbeitskraftanwerbern wohin sie auch gingen dort, wo sie zwischen den 1860er und 1920er Jahren den gesamten Golf von Guinea überquerten und hauptsächlich Kru von Liberien und Fang von Rio Muni, Kamerun und Gabon anwarben; und dort, wo sie ab den 1930er bis 1960er Jahren vor allem um die Bucht von Biafra eine noch nie dagewesene Anzahl an Vertragsarbeitern, vor allem Igbos und Ibibios aus dem südöstlichen Nigeria auf die florierenden Kakaoplantagen der Insel brachten. Die Anwerber tauchten vornehmlich als eine Modalität auf, die ich als ‘tout’ beschreibe und theoretisiere. Diese operierten fast ausschließlich mittels eines Exzesses an Sprache und Geld mittels Täuschung und informellen Vorschüssen. Zwar agierten sie ‘außerhalb’ des Rechts, doch erlaubte genau die Vertragsform von Fernando Pó, die langfristig und unwiderruflich zur Arbeit zwang, den Anwerbern die Ausübung ihrer Techniken. Eine Reihe an unerlaubten Verdrehungen wurden geschaffen und durchgereicht: Quasi-Versklavung durch Täuschung in Form von Kidnapping, Quasi-Schuldknechtschaft mittels informellen Lohnvorschüssen, die die Verträge ermöglichten sowie die grenz- und Arbeitsort überschreitende Migration einer relativ freien, allerdings flüchtigen Arbeitskraft. Der anhaltende Blick auf die ambivalenten Praktiken der Anwerber legt eine Reihe an Nebeneinandern von ‚frei’ und ‚unfrei’ offen, was kreative Potentiale für deren Intensivierung und Auflösung schuf, und über einzelne Punkten entlang eines Spektrums der freien-unfreien Arbeit hinausgeht.This dissertation follows Fernando Pó’s labour recruiters wherever they went— between the 1860s and 1920s recruiters traversed the entirety of the Gulf of Guinea and enlisted mostly Kru from Liberia and Fang from Rio Muni, Cameroon and Gabon; between the 1930s to 1960s they gathered particularly around the Bight of Biafra and brought an unprecedented number of contract workers into the island’s booming cacao plantations, mostly Igbos and Ibibios from south-eastern Nigeria. Recruiters tended to appear in a modality that I will describe and theorize as ‘touts’. They operated almost exclusively with an excess of language and money—deceit and informal advances. They operated ‘outside’ the law and the regulated, yet it was only the shape of the contract on Fernando Pó—forced, long and irrevocable—that allowed recruiters to deploy their techniques. Recruiters created and relayed a series of wholly impermissible twists: quasi-enslavement through fraud that was a form of kidnapping, quasi-debt bondage with informal wage advances enabled by the contracts, and even a movement of really quite free but fugitive labour across borders and work-sites. A sustained attention on the ambivalent practices of recruiters reveal a series of juxtapositions of free and unfree that produced creative potentials for intensification and unravelling, rather than single points along a ‘free-unfree’ labour spectrum

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum