Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable

Recognition of minimal unsatisfiable CNF formulas (unsatisfiable CNF formulas which become satisfiable if any clause is removed) is a classical DP-complete problem. It was shown recently that minimal unsatisfiable formulas with n variables and n+k clauses can be recognized in time . We improve this result and present an algorithm with time complexity ; hence the problem turns out to be fixed-parameter tractable (FTP) in the sense of Downey and Fellows (Parameterized Complexity, 1999). Our algorithm gives rise to a fixed-parameter tractable parameterization of the satisfiability problem: If for a given set of clauses F, the number of clauses in each of its subsets exceeds the number of variables occurring in the subset at most by k, then we can decide in time whether F is satisfiable; k is called the maximum deficiency of F and can be efficiently computed by means of graph matching algorithms. Known parameters for fixed-parameter tractable satisfiability decision are tree-width or related to tree-width. Tree-width and maximum deficiency are incomparable in the sense that we can find formulas with constant maximum deficiency and arbitrarily high tree-width, and formulas where the converse prevails

QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property

The QRAT (quantified resolution asymmetric tautology) proof system simulates virtually all inference rules applied in state of the art quantified Boolean formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding and deleting clauses and universal literals that have a certain redundancy property. To check for this redundancy property in QRAT, propositional unit propagation (UP) is applied to the quantifier free, i.e., propositional part of the QBF. We generalize the redundancy property in the QRAT system by QBF specific UP (QUP). QUP extends UP by the universal reduction operation to eliminate universal literals from clauses. We apply QUP to an abstraction of the QBF where certain universal quantifiers are converted into existential ones. This way, we obtain a generalization of QRAT we call QRAT+. The redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT based on UP. We report on proof theoretical improvements and experimental results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer, including appendi

Egg Formation in Lepidoptera

Reproductive biology in the Twentieth Century produced comprehensive descriptions of the mechanisms of egg formation in most of the major orders of insects. While many general principles of ovarian development and physiology emerged, every order turned out to have a set of its own special motifs. Discovery of the lepidopteran motifs is summarized in this essay. The emphasis is on developmental mechanisms, beginning with the early growth and differentiation of female germ cells and ending, after many turns in morphogenesis, physiology and biosynthesis, with eggs that are filled with yolk and encased in chorions. Examples of uniquely lepidopteran traits include the cellular composition of ovarian follicles, the number of tubular ovarioles in which they mature, the functions of cell-to-cell junctional complexes in their maturation, their use of glycosaminoglycans to maintain intercellular patency during vitellogenesis, the role of proton and calcium pumps in their ion physiology, a separate postvitellogenic period of water and inorganic ion uptake, and the fine structure and protein composition of their chorions. Discovery of this combination of idiosyncracies was based on advances in the general concepts and techniques of cell and molecular biology and on insights borrowed from studies on other insects. The lepidopteran ovary in turn has contributed much to the understanding of egg formation in insects generally

Approximate automata for omega-regular languages

Automata over infinite words, also known as ω -automata, play a key role in the verification and synthesis of reactive systems. The spectrum of ω -automata is defined by two characteristics: the acceptance condition (e.g. Büchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic ω -automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism. In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

The Phylogenetic Origin of oskar Coincided with the Origin of Maternally Provisioned Germ Plasm and Pole Cells at the Base of the Holometabola

The establishment of the germline is a critical, yet surprisingly evolutionarily labile, event in the development of sexually reproducing animals. In the fly Drosophila, germ cells acquire their fate early during development through the inheritance of the germ plasm, a specialized maternal cytoplasm localized at the posterior pole of the oocyte. The gene oskar (osk) is both necessary and sufficient for assembling this substance. Both maternal germ plasm and oskar are evolutionary novelties within the insects, as the germline is specified by zygotic induction in basally branching insects, and osk has until now only been detected in dipterans. In order to understand the origin of these evolutionary novelties, we used comparative genomics, parental RNAi, and gene expression analyses in multiple insect species. We have found that the origin of osk and its role in specifying the germline coincided with the innovation of maternal germ plasm and pole cells at the base of the holometabolous insects and that losses of osk are correlated with changes in germline determination strategies within the Holometabola. Our results indicate that the invention of the novel gene osk was a key innovation that allowed the transition from the ancestral late zygotic mode of germline induction to a maternally controlled establishment of the germline found in many holometabolous insect species. We propose that the ancestral role of osk was to connect an upstream network ancestrally involved in mRNA localization and translational control to a downstream regulatory network ancestrally involved in executing the germ cell program

Integrating Signals from the T-Cell Receptor and the Interleukin-2 Receptor

T cells orchestrate the adaptive immune response, making them targets for immunotherapy. Although immunosuppressive therapies prevent disease progression, they also leave patients susceptible to opportunistic infections. To identify novel drug targets, we established a logical model describing T-cell receptor (TCR) signaling. However, to have a model that is able to predict new therapeutic approaches, the current drug targets must be included. Therefore, as a next step we generated the interleukin-2 receptor (IL-2R) signaling network and developed a tool to merge logical models. For IL-2R signaling, we show that STAT activation is independent of both Src- and PI3-kinases, while ERK activation depends upon both kinases and additionally requires novel PKCs. In addition, our merged model correctly predicted TCR-induced STAT activation. The combined network also allows information transfer from one receptor to add detail to another, thereby predicting that LAT mediates JNK activation in IL-2R signaling. In summary, the merged model not only enables us to unravel potential cross-talk, but it also suggests new experimental designs and provides a critical step towards designing strategies to reprogram T cells

Viruses Associated with Ovarian Degeneration in Apis mellifera L. Queens

Queen fecundity is a critical issue for the health of honeybee (Apis mellifera L.) colonies, as she is the only reproductive female in the colony and responsible for the constant renewal of the worker bee population. Any factor affecting the queen's fecundity will stagnate colony development, increasing its susceptibility to opportunistic pathogens. We discovered a pathology affecting the ovaries, characterized by a yellow discoloration concentrated in the apex of the ovaries resulting from degenerative lesions in the follicles. In extreme cases, marked by intense discoloration, the majority of the ovarioles were affected and these cases were universally associated with egg-laying deficiencies in the queens. Microscopic examination of the degenerated follicles showed extensive paracrystal lattices of 30 nm icosahedral viral particles. A cDNA library from degenerated ovaries contained a high frequency of deformed wing virus (DWV) and Varroa destructor virus 1 (VDV-1) sequences, two common and closely related honeybee Iflaviruses. These could also be identified by in situ hybridization in various parts of the ovary. A large-scale survey for 10 distinct honeybee viruses showed that DWV and VDV-1 were by far the most prevalent honeybee viruses in queen populations, with distinctly higher prevalence in mated queens (100% and 67%, respectively for DWV and VDV-1) than in virgin queens (37% and 0%, respectively). Since very high viral titres could be recorded in the ovaries and abdomens of both functional and deficient queens, no significant correlation could be made between viral titre and ovarian degeneration or egg-laying deficiency among the wider population of queens. Although our data suggest that DWV and VDV-1 have a role in extreme cases of ovarian degeneration, infection of the ovaries by these viruses does not necessarily result in ovarian degeneration, even at high titres, and additional factors are likely to be involved in this pathology

A Honey Bee Hexamerin, HEX 70a, Is Likely to Play an Intranuclear Role in Developing and Mature Ovarioles and Testioles

Insect hexamerins have long been known as storage proteins that are massively synthesized by the larval fat body and secreted into hemolymph. Following the larval-to-pupal molt, hexamerins are sequestered by the fat body via receptor-mediated endocytosis, broken up, and used as amino acid resources for metamorphosis. In the honey bee, the transcript and protein subunit of a hexamerin, HEX 70a, were also detected in ovaries and testes. Aiming to identify the subcellular localization of HEX 70a in the female and male gonads, we used a specific antibody in whole mount preparations of ovaries and testes for analysis by confocal laser-scanning microscopy. Intranuclear HEX 70a foci were evidenced in germ and somatic cells of ovarioles and testioles of pharate-adult workers and drones, suggesting a regulatory or structural role. Following injection of the thymidine analog EdU we observed co-labeling with HEX 70a in ovariole cell nuclei, inferring possible HEX 70a involvement in cell proliferation. Further support to this hypothesis came from an injection of anti-HEX 70a into newly ecdysed queen pupae where it had a negative effect on ovariole thickening. HEX 70a foci were also detected in ovarioles of egg laying queens, particularly in the nuclei of the highly polyploid nurse cells and in proliferating follicle cells. Additional roles for this storage protein are indicated by the detection of nuclear HEX 70a foci in post-meiotic spermatids and spermatozoa. Taken together, these results imply undescribed roles for HEX 70a in the developing gonads of the honey bee and raise the possibility that other hexamerins may also have tissue specific functions