A complexity dichotomy for poset constraint satisfaction

In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free $\leq$-formulas. An instance of Poset-SAT($\Phi$) consists of finitely many variables $x_1,\ldots,x_n$ and formulas $\phi_i(x_{i_1},\ldots,x_{i_k})$ with $\phi_i \in \Phi$; the question is whether this input is satisfied by any partial order on $x_1,\ldots,x_n$ or not. We show that every such problem is NP-complete or can be solved in polynomial time, depending on $\Phi$. All Poset-SAT problems can be formalized as constraint satisfaction problems on reducts of the random partial order. We use model-theoretic concepts and techniques from universal algebra to study these reducts. In the course of this analysis we establish a dichotomy that we believe is of independent interest in universal algebra and model theory.Comment: 29 page

The Reducts of the Homogeneous Binary Branching C-relation

Let (L;C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C), i.e., the structures with domain L that are first-order definable in (L;C). We show that up to existential interdefinability, there are finitely many such reducts. This implies that there are finitely many reducts up to first-order interdefinability, thus confirming a conjecture of Simon Thomas for the special case of (L;C). We also study the endomorphism monoids of such reducts and show that they fall into four categories.Comment: 39 pages, 4 figure

Optimising the Solovay-Kitaev algorithm

The Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called "search space expansion", which modifies the initial stage of the Solovay-Kitaev algorithm, increasing the length of the possible approximating sequences but without requiring an exhaustive search over all possible sequences. We show that our technique, combined with a GNAT geometric tree search outputs gate sequences that are almost an order of magnitude smaller for the same level of accuracy. This therefore significantly reduces the error correction requirements for quantum algorithms on encoded fault-tolerant hardware.Comment: 9 page

Influence of temperature on mechanical characteristics of 1018 low carbon steel estimated by ultrasonic non-destructive testing method

The temperature dependence of ultrasonic velocities propagated in low carbon steel 1018 has been investigated by the A-scan mode of the ultrasonic non-destructive testing method. Experimental results show that these velocities are linearly dependent on temperature of the carbon steel sample in the range of 0 to 50 °C. Based on the experimental velocities of the longitudinal wave and the shear one, mechanical characteristics of this carbon steel including Poisson's ratio (υ), Young’s modulus (E), shear modulus (G), and bulk modulus (K) have been calculated. These mechanical characteristics have also been linear response with respect to the increase of sample’s temperature. By using linear fitting approach, the temperature dependence coefficients of these mechanical characteristics have been analyzed and estimated to be 9.76×10-6/°C, −0.057 GPa/°C, −0.023 GPa/°C, and −0.038 GPa/°C for v, E, G, and K, respectively. It is concluded that the influence of the temperature on the mechanical properties of the carbon steels is necessary determined due to the improved accuracy of the ultrasonic testing method

Trichinellosis in Vietnam

Trichinellosis is a zoonotic parasitic disease with a worldwide distribution. The aim of this work was to describe the epidemiological and clinical data of five outbreaks of trichinellosis, which affected ethnic minorities living in remote mountainous areas of northwestern Vietnam from 1970 to 2012. Trichinellosis was diagnosed in 126 patients, of which 11 (8.7%) were hospitalized and 8 (6.3%) died. All infected people had consumed raw pork from backyard and roaming pigs or wild boar at wedding, funeral, or New Year parties. The short incubation period (average of 9.5 days), the severity of the symptoms, which were characterized by diarrhea, abdominal pain, fever, myalgia, edema, weight loss, itch, and lisping, and the high mortality, suggest that patients had ingested a high number of larvae. The larval burden in pigs examined in one of the outbreaks ranged from 70 to 879 larvae/g. These larvae and those collected from a muscle biopsy taken from a patient from the 2012 outbreak were identified as Trichinella spiralis. Data presented in this work show that the northern regions of Vietnam are endemic areas for Trichinella infections in domestic pigs and humans