From algebra to logic: there and back again -- the story of a hierarchy

This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.Comment: Developments in Language Theory 2014, Ekaterinburg : Russian Federation (2014

On Hawking's Local Rigidity Theorems for Charged Black Holes

We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, R\'{a}cz and Wald, which was limited to the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field $T$ which tangent to the horizon and not vanishing on the bifurcate sphere, then space-time must be locally axially symmetric without the analyticity assumption. This axial symmetry plays a fundamental role in the classification theory of stationary black holes.Comment: 20 page

DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

Optimization in task--completion networks

We discuss the collective behavior of a network of individuals that receive, process and forward to each other tasks. Given costs they store those tasks in buffers, choosing optimally the frequency at which to check and process the buffer. The individual optimizing strategy of each node determines the aggregate behavior of the network. We find that, under general assumptions, the whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA

Future Foam

We study pocket universes which have zero cosmological constant and non-trivial boundary topology. These arise from bubble collisions in eternal inflation. Using a simplified dust model of collisions we find that boundaries of any genus can occur. Using a radiation shell model we perform analytic studies in the thin wall limit to show the existence of geometries with a single toroidal boundary. We give plausibility arguments that higher genus boundaries can also occur. In geometries with one boundary of any genus a timelike observer can see the entire boundary. Geometries with multiple disconnected boundaries can also occur. In the spherical case with two boundaries the boundaries are separated by a horizon. Our results suggest that the holographic dual description for eternal inflation, proposed by Freivogel, Sekino, Susskind and Yeh, should include summation over the genus of the base space of the dual conformal field theory. We point out peculiarities of this genus expansion compared to the string perturbation series.Comment: 23 pages, 6 figure

Vectorial Languages and Linear Temporal Logic

International audienceDetermining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently, especially when dealing with very large texts. Considering words as vectors and working on them using vectorial (parallel) operations allows to solve the problem faster than in linear time using sequential computations. In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends only on the language accepted by the automaton. We give precise characterizations of vectorial algorithms for star-free, solvable and regular languages in terms of the vectorial operations allowed. We also consider classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic. Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of linear-time temporal logic characterizing solvable and regular languages is PSPACE-complete

Church-Rosser Systems, Codes with Bounded Synchronization Delay and Local Rees Extensions

What is the common link, if there is any, between Church-Rosser systems, prefix codes with bounded synchronization delay, and local Rees extensions? The first obvious answer is that each of these notions relates to topics of interest for WORDS: Church-Rosser systems are certain rewriting systems over words, codes are given by sets of words which form a basis of a free submonoid in the free monoid of all words (over a given alphabet) and local Rees extensions provide structural insight into regular languages over words. So, it seems to be a legitimate title for an extended abstract presented at the conference WORDS 2017. However, this work is more ambitious, it outlines some less obvious but much more interesting link between these topics. This link is based on a structure theory of finite monoids with varieties of groups and the concept of local divisors playing a prominent role. Parts of this work appeared in a similar form in conference proceedings where proofs and further material can be found.Comment: Extended abstract of an invited talk given at WORDS 201

Thy-1 interaction with Fas in lipid rafts regulates fibroblast apoptosis and lung injury resolution.

Thy-1-negative lung fibroblasts are resistant to apoptosis. The mechanisms governing this process and its relevance to fibrotic remodeling remain poorly understood. By using either sorted or transfected lung fibroblasts, we found that Thy-1 expression is associated with downregulation of anti-apoptotic molecules Bcl-2 and Bcl-xL, as well as increased levels of cleaved caspase-9. Addition of rhFasL and staurosporine, well-known apoptosis inducers, caused significantly increased cleaved caspase-3, -8, and PARP in Thy-1-transfected cells. Furthermore, rhFasL induced Fas translocation into lipid rafts and its colocalization with Thy-1. These in vitro results indicate that Thy-1, in a manner dependent upon its glycophosphatidylinositol anchor and lipid raft localization, regulates apoptosis in lung fibroblasts via Fas-, Bcl-, and caspase-dependent pathways. In vivo, Thy-1 deficient (Thy1-/-) mice displayed persistence of myofibroblasts in the resolution phase of bleomycin-induced fibrosis, associated with accumulation of collagen and failure of lung fibrosis resolution. Apoptosis of myofibroblasts is decreased in Thy1-/- mice in the resolution phase. Collectively, these findings provide new evidence regarding the role and mechanisms of Thy-1 in initiating myofibroblast apoptosis that heralds the termination of the reparative response to bleomycin-induced lung injury. Understanding the mechanisms regulating fibroblast survival/apoptosis should lead to novel therapeutic interventions for lung fibrosis

Experimental functional response and inter-individual variation in foraging rate of teal (Anas crecca)

The functional response, i.e. the change in per capita food intake rate per time unit with changed food availability, is a widely used tool for understanding the ecology and behaviour of animals. However, waterfowl remain poorly explored in this context. In an aviary experiment we derived a functional response curve for teal (Anascrecca) foraging on rice (Oryzasativa) seeds. We found a linear relationship between intake rate and seed density, as expected for a filter-feeder. At high seed densities we found a threshold, above which intake rate still increased linearly but with a lower slope, possibly reflecting a switch from filter-feeding to a scooping foraging mode. The present study shows that food intake rate in teal is linearly related to food availability within the range of naturally occurring seed densities, a finding with major implications for management and conservation of wetland habitats.</p

Targeting Mitochondria by SS-31 Ameliorates the Whole Body Energy Status in Cancer- and Chemotherapy-Induced Cachexia

Cachexia is a complex metabolic syndrome frequently occurring in cancer patients and exacerbated by chemotherapy. In skeletal muscle of cancer hosts, reduced oxidative capacity and low intracellular ATP resulting from abnormal mitochondrial function were described. : The present study aimed at evaluating the ability of the mitochondria-targeted compound SS-31 to counteract muscle wasting and altered metabolism in C26-bearing (C26) mice either receiving chemotherapy (OXFU: oxaliplatin plus 5-fluorouracil) or not. : Mitochondrial dysfunction in C26-bearing (C26) mice associated with alterations of cardiolipin fatty acid chains. Selectively targeting cardiolipin with SS-31 partially counteracted body wasting and prevented the reduction of glycolytic myofiber area. SS-31 prompted muscle mitochondrial succinate dehydrogenase (SDH) activity and rescued intracellular ATP levels, although it was unable to counteract mitochondrial protein loss. Progressively increased dosing of SS-31 to C26 OXFU mice showed transient (21 days) beneficial effects on body and muscle weight loss before the onset of a refractory end-stage condition (28 days). At day 21, SS-31 prevented mitochondrial loss and abnormal autophagy/mitophagy. Skeletal muscle, liver and plasma metabolomes were analyzed, showing marked energy and protein metabolism alterations in tumor hosts. SS-31 partially modulated skeletal muscle and liver metabolome, likely reflecting an improved systemic energy homeostasis. : The results suggest that targeting mitochondrial function may be as important as targeting protein anabolism/catabolism for the prevention of cancer cachexia. With this in mind, prospective multi-modal therapies including SS-31 are warranted