Robustly Solvable Constraint Satisfaction Problems

An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least $(1-g(\varepsilon))$-fraction of the constraints given a $(1-\varepsilon)$-satisfiable instance, where $g(\varepsilon) \rightarrow 0$ as $\varepsilon \rightarrow 0$. Guruswami and Zhou conjectured a characterization of constraint languages for which the corresponding constraint satisfaction problem admits an efficient robust algorithm. This paper confirms their conjecture

Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem

The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete otherwise. This paper provides two new characterizations of finitely generated Taylor varieties. The first characterization is using absorbing subalgebras and the second one cyclic terms. These new conditions allow us to reprove the conjecture of Bang-Jensen and Hell (proved by the authors) and the characterization of locally finite Taylor varieties using weak near-unanimity terms (proved by McKenzie and Mar\'oti) in an elementary and self-contained way

Neutrophil Extracellular Traps in Infectious Human Diseases

Neutrophils, as the main cells of the first line of host defense against microbial pathogens, are responsible for pathogen recognition, inhibition of pathogen spreading into the host tissue, and finally, killing the invader cells. Neutrophils carry out these functions via numerous mechanisms, including a relatively recently described activity based on a release of neutrophil extracellular traps (NETs), a process called netosis. NETs are structures composed of DNA backbone, decorated with antimicrobial factors, derived from neutrophil granules. The structure of NETs and their enzymatic and microbicidal inclusions enable efficient trapping and killing of microorganisms within the neutrophil extracellular space. However, the efficiency of NETs depends on neutrophil ability to recognize pathogen signals and to trigger rapid responses. In this chapter, we focus on possible pathways involved in the release of NETs and summarize the current knowledge on triggers of this process during bacterial, fungal, protozoan, and viral infections. We also consider the mechanisms used by microorganisms to evade NET-killing activity and analyze the harmful potential of NETs against the host cells and the contribution of NETs to noninfectious human diseases

Selected mucolytic, anti-inflammatory and cardiovascular drugs change the ability of neutrophils to form extracellular traps (NETs)

Neutrophils form the first line of host defense against infections that combat pathogens using two major mechanisms, the phagocytosis or the release of neutrophil extracellular traps (NETs). The netosis (NET formation) exerts additional, unfavorable effects on the fitness of host cells and is also involved at the sites of lung infection, increasing the mucus viscosity and in the circulatory system where it can influence the intravascular clot formation. Although molecular mechanisms underlying the netosis are still incompletely understood, a role of NADPH oxidase that activates the production of reactive oxygen species (ROS) during the initiation of NETs has been well documented. Since several commonly used drugs can affects the netosis, our current study was aimed to determine the effects of selected mucolytic, anti-inflammatory and cardiovascular drugs on NET formation, with a special emphasis on ROS production and NADPH oxidase activity. The treatment of neutrophils with N-acetylcysteine, ketoprofen and ethamsylate reduced the production of ROS by these cells in a dose-dependent manner. NET formation was also modulated by selected drugs. N-acetylcysteine inhibited the netosis but in the presence of H2O2 this neutrophil ability was restored, indicating that N-acetylcysteine may influence the NET formation by modulating ROS productivity. The administration of ethamsylate led to a significant reduction in NET formation and this effect was not restored by H2O2 or S. aureus, suggesting the unexpected additional side effects of this drug. Ketoprofen seemed to promote ROS-independent NET release, simultaneously inhibiting ROS production. The results, obtained in this study strongly suggest that the therapeutic strategies applied in many neutrophil-mediated diseases should take into account the NET-associated effects

The subpower membership problem for semigroups

Fix a finite semigroup $S$ and let $a_1,\ldots,a_k, b$ be tuples in a direct power $S^n$. The subpower membership problem (SMP) asks whether $b$ can be generated by $a_1,\ldots,a_k$. If $S$ is a finite group, then there is a folklore algorithm that decides this problem in time polynomial in $nk$. For semigroups this problem always lies in PSPACE. We show that the SMP for a full transformation semigroup on 3 letters or more is actually PSPACE-complete, while on 2 letters it is in P. For commutative semigroups, we provide a dichotomy result: if a commutative semigroup $S$ embeds into a direct product of a Clifford semigroup and a nilpotent semigroup, then SMP(S) is in P; otherwise it is NP-complete

Absorption in Universal Algebra and CSP

The algebraic approach to Constraint Satisfaction Problem led to many developments in both CSP and universal algebra. The notion of absorption was successfully applied on both sides of the connection. This article introduces the concept of absorption, illustrates its use in a number of basic proofs and provides an overview of the most important results obtained by using it

Neutrophil extracellular traps (NETs) : formation and implications

Neutrophils are cells of the immune system which freely circulate in blood vessels and are recruited to the inflammation sites when the human organism responds to microbial infections. One of the mechanisms of neutrophil action is the formation of neutrophil extracellular traps (NETs) The process of NET generation, called netosis, is a specific type of cell death, different from necrosis and apoptosis. NETs are formed by neutrophils upon contact with various bacteria or fungi as well as with activated platelets or under the influence of numerous inflammatory stimuli, and this process is associated with dramatic changes in the morphology of the cells. The main components of NETs, DNA and granular antimicrobial proteins, determine their antimicrobial properties. The pathogens trapped in NETs are killed by oxidative and non-oxidative mechanisms. On the other hand, it was also discovered that chromatin and proteases released into the circulatory system during NET formation can regulate procoagulant and prothrombotic factors and take part in clot formation in blood vessels. NETs have also been detected in lungs where they are involved in chronic inflammation processes in ALI/ARDS patients. Moreover, DNA-proteins complexes have been found in the airway fluids of cystic fibrosis patients where they can increase the viscosity of the sputum and have a negative impact on the lung functions. The DNA-complexed granular proteins and other proteins released by neutrophils during netosis lead to autoimmunity syndromes such as systemic lupus erythematosus (SLE), small-vessel vasculitis (SVV) or autoimmune diseases associated with the formation of autoantibodies against chromatin and neutrophil components. A possible involvement of NETs in metastasis is also considered

Dichotomy for Symmetric Boolean PCSPs

In one of the most actively studied version of Constraint Satisfaction Problem, a CSP is defined by a relational structure called a template. In the decision version of the problem the goal is to determine whether a structure given on input admits a homomorphism into this template. Two recent independent results of Bulatov [FOCS\u2717] and Zhuk [FOCS\u2717] state that each finite template defines CSP which is tractable or NP-complete. In a recent paper Brakensiek and Guruswami [SODA\u2718] proposed an extension of the CSP framework. This extension, called Promise Constraint Satisfaction Problem, includes many naturally occurring computational questions, e.g. approximate coloring, that cannot be cast as CSPs. A PCSP is a combination of two CSPs defined by two similar templates; the computational question is to distinguish a YES instance of the first one from a NO instance of the second. The computational complexity of many PCSPs remains unknown. Even the case of Boolean templates (solved for CSP by Schaefer [STOC\u2778]) remains wide open. The main result of Brakensiek and Guruswami [SODA\u2718] shows that Boolean PCSPs exhibit a dichotomy (PTIME vs. NPC) when "all the clauses are symmetric and allow for negation of variables". In this paper we remove the "allow for negation of variables" assumption from the theorem. The "symmetric" assumption means that changing the order of variables in a constraint does not change its satisfiability. The "negation of variables" means that both of the templates share a relation which can be used to effectively negate Boolean variables. The main result of this paper establishes dichotomy for all the symmetric boolean templates. The tractability case of our theorem and the theorem of Brakensiek and Guruswami are almost identical. The main difference, and the main contribution of this work, is the new reason for hardness and the reasoning proving the split