Decomposing quantified conjunctive (or disjunctive) formulas

Model checking---deciding if a logical sentence holds on a structure---is a basic computational task that is well known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable based on a novel generalization of treewidth that generalizes and places into a unified framework a number of existing results

A Dichotomy Theorem for the Approximate Counting of Complex-Weighted Bounded-Degree Boolean CSPs

We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1) constraints, particularly, when degrees of input instances are bounded from above by a fixed constant. All degree-1 counting CSPs are obviously solvable in polynomial time. When the instance's degree is more than two, we present a dichotomy theorem that classifies all counting CSPs admitting free unary constraints into exactly two categories. This classification theorem extends, to complex-weighted problems, an earlier result on the approximation complexity of unweighted counting Boolean CSPs of bounded degree. The framework of the proof of our theorem is based on a theory of signature developed from Valiant's holographic algorithms that can efficiently solve seemingly intractable counting CSPs. Despite the use of arbitrary complex weight, our proof of the classification theorem is rather elementary and intuitive due to an extensive use of a novel notion of limited T-constructibility. For the remaining degree-2 problems, in contrast, they are as hard to approximate as Holant problems, which are a generalization of counting CSPs.Comment: A4, 10pt, 20 pages. This revised version improves its preliminary version published under a slightly different title in the Proceedings of the 4th International Conference on Combinatorial Optimization and Applications (COCOA 2010), Lecture Notes in Computer Science, Springer, Vol.6508 (Part I), pp.285--299, Kailua-Kona, Hawaii, USA, December 18--20, 201

Extruded scintillator for the Calorimetry applications

An extrusion line has been installed and successfully operated at FNAL (Fermi National Accelerator Laboratory) in collaboration with NICADD (Northern Illinois Center for Accelerator and Detector Development). This new Facility will serve to further develop and improve extruded plastic scintillator. Recently progress has been made in producing co-extruded plastic scintillator, thus increasing the potential HEP applications of this Facility. The current R&D work with extruded and co-extruded plastic scintillator for a potential ALICE upgrade, the ILC calorimetry program and the MINERvA experiment show the attractiveness of the chosen strategy for future experiments and calorimetry. We extensively discuss extruded and co-extruded plastic scintillator in calorimetry in synergy with new Solid State Photomultipliers. The characteristics of extruded and co-extruded plastic scintillator will be presented here as well as results with non-traditional photo read-ou

Solving order constraints in logarithmic space.

We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space

Optimum morphology of gold nanorods for light-induced hyperthermia

Owing to their unique chemical and physical properties, colloidal gold nanoparticles have prompted a wide variety of biocompatible nano-agents for cancer imaging, diagnosis and treatment. In this context, biofunctionalized gold nanorods (AuNRs) are promising candidates for light-induced hyperthermia, to cause local and selective damage in malignant tissue. Yet, the efficacy of AuNR-based hyperthermia is highly dependent on several experimental parameters; in particular, the AuNR morphology strongly affects both physical and biological involved processes. In the present work, we systematically study the influence of different structural parameters like the AuNR aspect ratio, length and molecular weight on in vitro cytotoxicity, cellular uptake and heat generation efficiency. Our results enable us to identify the optimum AuNR morphology to be used for in vivo hyperthermia treatment.Postprint (author's final draft

The Hardness of Embedding Grids and Walls

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a subgraph of $H$) is fixed-parameter tractable if $K$ is a class of graphs of bounded tree width and $W[1]$-complete otherwise. Towards this conjecture, we prove that the embedding problem is $W[1]$-complete if $K$ is the class of all grids or the class of all walls

On the reduction of the CSP dichotomy conjecture to digraphs

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. We also show that our reduction preserves the bounded width property, i.e., solvability by local consistency methods. We discuss further algorithmic properties that are preserved and related open problems.Comment: 34 pages. Article is to appear in CP2013. This version includes two appendices with proofs of claims omitted from the main articl

Robust algorithms with polynomial loss for near-unanimity CSPs

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a xed domain to the variables so that all constraints are satised. In the optimization version, the goal is to maximize the number of satised constraints. An approximation algorithm for CSP is called robust if it outputs an assignment satisfying an (1????g("))-fraction of constraints on any (1????")-satisable instance, where the loss function g is such that g(") ! 0 as " ! 0. We study how the robust approximability of CSPs depends on the set of constraint relations allowed in instances, the so-called constraint language. All constraint languages admitting a robust polynomial-time algorithm (with some g) have been characterised by Barto and Kozik, with the general bound on the loss g being doubly exponential, specically g(") = O((log log(1="))= log(1=")). It is natural to ask when a better loss can be achieved: in particular, polynomial loss g(") = O("1=k) for some constant k. In this paper, we consider CSPs with a constraint language having a nearunanimity polymorphism. This general condition almost matches a known necessary condition for having a robust algorithm with polynomial loss. We give two randomized robust algorithms with polynomial loss for such CSPs: one works for any near-unanimity polymorphism and the parameter k in the loss depends on the size of the domain and the arity of the relations in ????, while the other works for a special ternary near-unanimity operation called dual discriminator with k = 2 for any domain size. In the latter case, the CSP is a common generalisation of Unique Games with a xed domain and 2-Sat. In the former case, we use the algebraic approach to the CSP. Both cases use the standard semidenite programming relaxation for CSP

Uncertainty estimation of road-dust emissions via interval statistics

Particulate matter, a.k.a. particle pollution, is a complex mixture of small particles and liquid droplets that are present in the air. Once inhaled, these particles can affect the heart and lungs and cause serious health problems. A recent study, based on geographically referenced datasets of pollutant emissions has shown that non-exhaust related pollution is at present dominant and increasing. Emissions from paved roads are poorly estimated due to the lack of knowledge about the resuspension process. Recent literature works have attempted to provide a reliable framework for the estimation of emission factors. Estimations are obtained by linear regression with a single-valued discriminant for the acceptance/rejection of the experimental dataset based on the evaluation of the r-squared coefficient. In this paper, we explore alternative methods to evaluate the "quality" of the data and consequently discriminate whether a given sample can be accepted to provide estimation of the emission factors. Uncertainties are characterised both in the data and in the statistical model. Measurements are expressed with interval-valued datapoints to include the experiment precision directly within the estimation process. Alternative fitting techniques that avoid the use a single-valued discriminant are also explored for an inclusive estimation of the emission factors