Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

Numerical study of surface-induced reorientation and smectic layering in a nematic liquid crystal

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order is rapidly decaying when moving away from the surface, the uniaxial nematic order parameter shows an oscillatory behavior close to the substrate, accompanied by a non-zero local biaxiality.Comment: LaTeX, 17 pages, with 4 postscript figure

Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D ±J\pm J Ising Spin Glass

The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When $L$ is even, almost all domain walls have energy $E_{dw}$ = 0 or 4. When $L$ is odd, most domain walls have $E_{dw}$ = 2. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. When $E_{dw} = 0$, the probability distribution of $|S_{dw}|$ is approximately exponential. The variance of this distribution is proportional to $L$, in agreement with the results of Saul and Kardar. For $E_{dw} = k > 0$ the distribution of $S_{dw}$ is not symmetric about zero. In these cases the variance still appears to be linear in $L$, but the average of $S_{dw}$ grows faster than $\sqrt{L}$. This suggests a one-parameter scaling form for the $L$-dependence of the distributions of $S_{dw}$ for $k > 0$.Comment: 13 page

Clinicopathological determinants of an elevated systemic inflammatory response following elective potentially curative resection for colorectal cancer

Introduction: The postoperative systemic inflammatory response (SIR) is related to both long- and short-term outcomes following surgery for colorectal cancer. However, it is not clear which clinicopathological factors are associated with the magnitude of the postoperative SIR. The present study was designed to determine the clinicopathological determinants of the postoperative systemic inflammatory response following colorectal cancer resection. Methods: Patients with a histologically proven diagnosis of colorectal cancer who underwent elective, potentially curative resection during a period from 1999 to 2013 were included in the study (n = 752). Clinicopathological data and the postoperative SIR, as evidenced by postoperative Glasgow Prognostic Score (poGPS), were recorded in a prospectively maintained database. Results: The majority of patients were aged 65 years or older, male, were overweight or obese, and had an open resection. After adjustment for year of operation, a high day 3 poGPS was independently associated with American Society of Anesthesiologists (ASA) grade (hazard ratio [HR] 1.96; confidence interval [CI] 1.25–3.09; p = 0.003), body mass index (BMI) (HR 1.60; CI 1.07–2.38; p = 0.001), mGPS (HR 2.03; CI 1.35–3.03; p = 0.001), and tumour site (HR 2.99; CI 1.56–5.71; p < 0.001). After adjustment for year of operation, a high day 4 poGPS was independently associated with ASA grade (HR 1.65; CI 1.06–2.57; p = 0.028), mGPS (HR 1.81; CI 1.22–2.68; p = 0.003), NLR (HR 0.50; CI 0.26–0.95; p = 0.034), and tumour site (HR 2.90; CI 1.49–5.65; p = 0.002). Conclusions: ASA grade, BMI, mGPS, and tumour site were consistently associated with the magnitude of the postoperative systemic inflammatory response, evidenced by a high poGPS on days 3 and 4, in patients undergoing elective potentially curative resection for colorectal cancer

Preoperative systemic inflammation predicts postoperative infectious complications in patients undergoing curative resection for colorectal cancer

The presence of systemic inflammation before surgery, as evidenced by the glasgow prognostic score (mGPS), predicts poor long-term survival in colorectal cancer. The aim was to examine the relationship between the preoperative mGPS and the development of postoperative complications in patients undergoing potentially curative resection for colorectal cancer. Patients (n=455) who underwent potentially curative resections between 2003 and 2007 were assessed consecutively, and details were recorded in a database. The majority of patients presented for elective surgery (85%) were over the age of 65 years (70%), were male (58%), were deprived (53%), and had TNM stage I/II disease (61%), had preoperative haemoglobin (56%), white cell count (87%) and mGPS 0 (58%) in the normal range. After surgery, 86 (19%) patients developed a postoperative complication; 70 (81%) of which were infectious complications. On multivariate analysis, peritoneal soiling (P<0.01), elevated preoperative white cell count (P<0.05) and mGPS (P<0.01) were independently associated with increased risk of developing a postoperative infection. In elective patients, only the mGPS (OR=1.75, 95% CI=1.17-2.63, P=0.007) was significantly associated with increased risk of developing a postoperative infection. Preoperative elevated mGPS predicts increased postoperative infectious complications in patients undergoing potentially curative resection for colorectal cancer

The Hudson-Raritan Estuary as a crossroads for distribution of blue (Callinectes sapidus), lady (Ovalipes ocellatus), and Atlantic rock (Cancer irroratus) crabs

Blue (Callinectes sapidus)(Portunidae),lady (Ovalipes ocellatus)(Portunidae), and Atlantic rock (Cancer irroratus) (Cancridae) crabs inhabit estuaries on the northeast United States coast for parts or all of their life cycles. Their distributions overlap or cross during certain seasons. During a 1991–1994 monthly otter trawl survey in the Hudson-Raritan Estuary between New York and New Jersey, blue and lady crabs were collected in warmer months and Atlantic rock crabs in colder months. Sex ratios, male:female, of mature crabs were 1:2.0 for blue crabs, 1:3.1 for lady crabs, and 21.4:1 for Atlantic rock crabs. Crabs, 1286 in total, were subsampled for dietary analysis, and the dominant prey taxa for all crabs, by volume of foregut contents, were mollusks and crustaceans. The proportion of amphipods and shrimp in diets decreased as crab size increased. Trophic niche breadth was widest for blue crabs, narrower for lady crabs, and narrowest for Atlantic rock crabs. Trophic overlap was lowest between lady crabs and Atlantic rock crabs, mainly because of frequent consumption of the dwarf surfclam (Mulinia lateralis) by the former and the blue mussel (Mytilus edulis) by the latter. The result of cluster analysis showed that size class and location of capture of predators in the estuary were more influential on diet than the species or sex of the predators

Strong Enhancement of Superconducting Correlation in a Two-Component Fermion Gas

We study high-density electron-hole (e-h) systems with the electron density slightly larger than the hole density. We find a new superconducting phase, in which the excess electrons form Cooper pairs moving in an e-h BCS phase. The coexistence of the e-h and e-e orders is possible because e and h have opposite charges, whereas analogous phases are impossible in the case of two fermion species that have the same charge or are neutral. Most strikingly, the e-h order enhances the superconducting e-h order parameter by more than one order of magnitude as compared with that given by the BCS formula, for the same value of the effective e-e attractive potential \lambda^{ee}. This new phase should be observable in an e-h system created by photoexcitation in doped semiconductors at low temperatures.Comment: 5 pages including 5 PostScript figure

Tunneling spectra of strongly coupled superconductors: Role of dimensionality

We investigate numerically the signatures of collective modes in the tunneling spectra of superconductors. The larger strength of the signatures observed in the high-Tc superconductors, as compared to classical low-Tc materials, is explained by the low dimensionality of these layered compounds. We also show that the strong-coupling structures are dips (zeros in the d2I/dV2 spectrum) in d-wave superconductors, rather than the steps (peaks in d2I/dV2) observed in classical s-wave superconductors. Finally we question the usefulness of effective density of states models for the analysis of tunneling data in d-wave superconductors.Comment: 8 pages, 6 figure

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Theory of Tunneling for Rough Junctions

A formally exact expression for the tunneling current, for its separation into specular and diffuse components, and for its directionality, is given for a thick tunnel junction with rough interfaces in terms of the properties of appropriately defined scattering amplitudes. An approximate evaluation yields the relative magnitudes of the specular and diffuse components, and the angular dependence of the diffuse component, in terms of certain statistical properties of the junction interfaces.Comment: 4 page