The k-variable property is stronger than H-dimension k

Accepted versio

Randomisation and Derandomisation in Descriptive Complexity Theory

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from PTIME. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. Similarly, we present a query on ordered structures which is definable in BPFO but not in monadic second-order logic, and a query on additive structures which is definable in BPFO but not in FO. The latter of these queries shows that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixed-point logic with counting, captures the complexity class BPP, even on unordered structures

Impaired haematopoietic stem cell differentiation and enhanced skewing towards myeloid progenitors in aged caspase-2-deficient mice

The apoptotic cysteine protease caspase-2 has been shown to suppress tumourigenesis in mice and its reduced expression correlates with poor prognosis in some human malignancies. Caspase-2-deficient mice develop normally but show ageing-related traits and, when challenged by oncogenic stimuli or certain stress, show enhanced tumour development, often accompanied by extensive aneuploidy. As stem cells are susceptible to acquiring age-related functional defects because of their self-renewal and proliferative capacity, we examined whether loss of caspase-2 promotes such defects with age. Using young and aged Casp2−/− mice, we demonstrate that deficiency of caspase-2 results in enhanced aneuploidy and DNA damage in bone marrow (BM) cells with ageing. Furthermore, we demonstrate for the first time that caspase-2 loss results in significant increase in immunophenotypically defined short-term haematopoietic stem cells (HSCs) and multipotent progenitors fractions in BM with a skewed differentiation towards myeloid progenitors with ageing. Caspase-2 deficiency leads to enhanced granulocyte macrophage and erythroid progenitors in aged mice. Colony-forming assays and long-term culture-initiating assay further recapitulated these results. Our results provide the first evidence of caspase-2 in regulating HSC and progenitor differentiation, as well as aneuploidy, in vivo.Swati Dawar, Nur Hezrin Shahrin, Nikolina Sladojevic, Richard J D, Andrea, Loretta Dorstyn, Devendra K Hiwase and Sharad Kuma

Reconfiguration on sparse graphs

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is possible to transform S into T by a sequence of vertex additions and deletions such that each intermediate set is also a feasible solution of size bounded by k. We study reconfiguration variants of two classical vertex-subset problems, namely Independent Set and Dominating Set. We denote the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete on graphs of bounded bandwidth and W[1]-hard parameterized by k on general graphs. We show that ISR is fixed-parameter tractable parameterized by k when the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we answer positively an open question concerning the parameterized complexity of the problem on graphs of bounded treewidth. Moreover, our techniques generalize recent results showing that ISR is fixed-parameter tractable on planar graphs and graphs of bounded degree. For DSR, we show the problem fixed-parameter tractable parameterized by k when the input graph does not contain large bicliques, a class of graphs which includes graphs of bounded degeneracy and nowhere-dense graphs

Disconnection clauses: an inevitable symptom of regionalism?

‘Disconnection clauses’ are legal provisions inserted into multilateral conventions to ensure that certain parties to the convention are not required to apply the rules of the convention because other relevant rules have already been agreed to among themselves. A disconnection clause can also be described more generally as a ‘conflict clause’ because it signals to all parties that parallel and potentially conflicting treaty obligations exist. This paper presents a discussion of the disconnection clause which argues that while these clauses make it possible for a limited group of parties to enhance the objectives of a treaty by taking measures that correspond to their special circumstance, this practice also creates a possibility that the inter se agreement will undermine the original treaty regime. The actual impact of a particular disconnection clause depends on how the clause is crafted, along with the changing nature of the regime that it refers to. The potential for a disconnection clause to undermine the object and purpose of the original treaty can therefore be removed during its design. Nevertheless, without full disclosure when negotiating the convention, any clause that seeks to replace treaty provisions with an alternative regime that would be applicable only between certain parties may, at worst, be creating different standards for different parties and, at best, be opaque and incoherent. This paper first describes the various types of disconnection clause, focusing on their purpose and development. It then assesses the main legal and political controversies surrounding these clauses before assessing whether these clauses could potentially create more legal problems than they are intended to solve or whether they are simply a practical response to deepening regionalism

Contraction Bidimensionality: the Accurate Picture

We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory -- the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters

Fixed-Parameter Tractable Distances to Sparse Graph Classes

We show that for various classes $\mathcal{C}$ of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph $\small{G}$ to $\mathcal{C}$ is fixed-parameter tractable. The results are based on two general techniques. The first of these, building on recent work of Grohe et al. establishes that any class of graphs that is slicewise nowhere dense and slicewise first-order definable is FPT. The second shows that determining the elimination distance of a graph $\small{G}$ to a minor-closed class $\mathcal{C}$ is FPT. We demonstrate that several prior results (of Golovach, Moser and Thilikos and Mathieson) on the fixed-parameter tractability of distance measures are special cases of our first method

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

CuInSe2 thin films produced by rf sputtering in Ar/H2 atmospheres

Structural, compositional, optical, and electrical properties of CuInSe2thin filmsgrown by rf reactive sputtering from a Se excess target in Ar/H2 atmospheres are presented. The addition of H2 to the sputtering atmospheres allows the control of stoichiometry of films giving rise to remarkable changes in the film properties. Variation of substrate temperature causes changes in film composition because of the variation of hydrogen reactivity at the substrate. Measurements of resistivity at variable temperatures indicate a hopping conduction mechanism through gap states for films grown at low temperature (100–250 °C), the existence of three acceptor levels at about 0.046, 0.098, and 0.144 eV above valence band for films grown at intermediate temperature (250–350 °C), and a pseudometallic behavior for film grown at high temperatures (350–450 °C). Chalcopyrite polycrystalline thin films of CuInSe2 with an average grain size of 1 μm, an optical gap of 1.01 eV, and resistivities from 10− 1 to 103 Ω cm can be obtained by adding 1.5% of H2 to the sputtering atmosphere and by varying the substrate temperature from 300 to 400 °C