Sum Of Lines Research Articles

A linear time approach to three-dimensional reconstruction by discrete tomography

The goal of discrete tomography is to reconstruct an unknown function $f$ via a given set of line sums. In addition to requiring accurate reconstructions, it is favourable to be able to perform the task in a timely manner. This is complicated by the presence of ghosts, which allow many solutions to exist in general. In this paper we consider the case of a function $f : A \to \mathbb{R}$ where $A$ is a finite grid in $\mathbb{Z}^3$. Previous work has shown that in the two-dimensional case it is possible to determine all solutions in parameterized form in linear time (with respect to the number of directions and the grid size) regardless of whether the solution is unique. In this work, we show that a similar linear method exists in three dimensions under the condition of nonproportionality. We show that the condition of nonproportionality is fulfilled in the case of three-dimensional boundary ghosts.

Uniqueness and reconstruction of finite lattice sets from their line sums

If an unknown finite set C⊂Z2 is cut by lines parallel to given directions, then one may count the number of points of C that are intercepted by each line, that is, the projections of C in the given directions. The inverse problem consists in reconstructing the set C, interpreted as a binary image, from the knowledge of its projections.In general, this challenging combinatorial problem, also related to the tomographic reconstruction of an unknown homogeneous object by means of X-rays, is ill-posed, meaning that different binary images exist that match the available projections. Therefore, as a preliminary step, one can try to find conditions to be imposed on the considered directions in order to limit the number of allowed solutions.In this paper we address the above problems for sets C contained in a finite assigned lattice grid, and generalize some results known in literature.First, we describe special sets of lattice directions, called simple cycles, and focus on some of their properties. Then we prove that uniqueness of reconstruction for binary images is guaranteed if and only if the line sums are computed along suitable simple cycles having even cardinality.As a second item, we prove that the unique binary solution can be explicitly reconstructed from a real-valued solution having minimal Euclidean norm. This leads to an explicit reconstruction algorithm, tested on four different phantoms and compared with previous results, which points out a significant improvement of the corresponding performance.

Experimental confirmation of the formation of collective modes of the magnetization motion of paramagnetic particles in dilute solutions due to spin exchange

Experimental confirmation of the manifestations of new spin exchange paradigm in EPR spectra of 14N nitroxide radical solutions is presented. It was shown that in the region of relatively low concentrations of radicals, the two side components of the spectrum have a mixed shape (the sum of the absorptive line and dispersive line). The dispersion contributions in these two lines have opposite signs. As the concentration of radicals increases, the contribution of dispersion passes through an extremum and in the region of maximum contribution of dispersion, the contribution of absorption to these two lines changes sign. In the region of high concentrations of radicals, when one homogeneously broadened line is practically observed, it turns out that these side components have resonant frequencies that do not coincide with the frequency of the center of gravity of the spectrum.

Numerical Performance of Correlated-k Distribution Method in Atmospheric Escape Simulation

Atmospheric escape is crucial to understanding the evolution of planets in and out of the solar system and to interpreting atmospheric observations. While hydrodynamic escape simulations have been actively developed incorporating detailed processes such as UV heating, chemical reactions, and radiative cooling, the radiative cooling by molecules has been treated as emission from selected lines or rotational/vibrational bands to reduce its numerical cost. However, ad hoc selections of radiative lines would risk estimating inaccurate cooling rates because important lines or wavelengths for atmospheric cooling depend on emitting conditions such as temperature and optical thickness. In this study, we apply the correlated-k distribution (CKD) method to cooling rate calculations for H2-dominant transonic atmospheres containing H2O or CO as radiative species, to investigate its numerical performance and the importance of considering all lines of the molecules. Our simulations demonstrate that the sum of weak lines, which provides only 1% of the line emission energy in total at optically thin conditions, can become the primary source of radiative cooling in optically thick regions, especially for H2O-containing atmospheres. Also, in our hydrodynamic simulations, the CKD method with a wavelength resolution of 1000 is found to be effective, allowing the calculation of escape rate and temperature profiles with acceptable numerical cost. Our results show the importance of treating all radiative lines and the usefulness of the CKD method in hydrodynamic escape simulations. It is particularly practical for heavy-element-enriched atmospheres considered in small exoplanets, including super-Earths, without any prior selections for effective lines.

Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability

Abstract In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for $d=2,3,4$ , these K-moduli of pairs are isomorphic to the K-moduli spaces of del Pezzo surfaces. For $d=1$ , we prove that they are different by exhibiting some walls.

Generic Torelli and local Schottky theorems for Jacobian elliptic surfaces

Suppose that $f:X\to C$ is a general Jacobian elliptic surface over ${\mathbb {C}}$ of irregularity $q$ and positive geometric genus $h$. Assume that $10 h>12(q-1)$, that $h>0$ and let $\overline {\mathcal {E}\ell \ell }$ denote the stack of generalized elliptic curves. (1) The moduli stack $\mathcal {JE}$ of such surfaces is smooth at the point $X$ and its tangent space $T$ there is naturally a direct sum of lines $(v_a)_{a\in Z}$, where $Z\subset C$ is the ramification locus of the classifying morphism $\phi :C\to \overline {\mathcal {E}\ell \ell }$ that corresponds to $X\to C$. (2) For each $a\in Z$ the map $\overline {\nabla }_{v_a}:H^{2,0}(X)\to H^{1,1}_{\rm prim}(X)$ defined by the derivative $per_*$ of the period map $per$ is of rank one. Its image is a line ${\mathbb {C}}[\eta _a]$ and its kernel is $H^0(X,\Omega ^2_X(-E_a))$, where $E_a=f^{-1}(a)$. (3) The classes $[\eta _a]$ form an orthogonal basis of $H^{1,1}_{\rm prim}(X)$ and $[\eta _a]$ is represented by a meromorphic $2$-form $\eta _a$ in $H^0(X,\Omega ^2_X(2E_a))$ of the second kind. (4) We prove a local Schottky theorem; that is, we give a description of $per_*$ in terms of a certain additional structure on the vector bundles that are involved. Assume further that $8h>10(q-1)$ and that $h\ge q+3$. (5) Given the period point $per(X)$ of $X$ that classifies the Hodge structure on the primitive cohomology $H^2_{\rm prim}(X)$ and the image of $T$ under $per_*$ we recover $Z$ as a subset of ${\mathbb {P}}^{h-1}$ and then, by quadratic interpolation, the curve $C$. (6) We prove a generic Torelli theorem for these surfaces. Everything relies on the construction, via certain kinds of Schiffer variations of curves, of certain variations of $X$ for which $per_*$ can be calculated. (In an earlier version of this paper we used variations constructed by Fay. However, Schiffer variations are slightly more powerful.)

Error Correction for Discrete Tomography

Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A → R where A is a finite subset of ℤ2 and R an integral domain. Several reconstruction methods have been introduced in the literature. Recently Ceko, Pagani and Tijdeman developed a fast method to reconstruct a function with the same line sums as f. Up to here we assumed that the line sums are exact. Some authors have developed methods to recover the function f under suitable conditions by using the redundancy of data. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than d/2 errors can be corrected and that this bound is the best possible. Moreover, we prove that if it is known that the line sums in k given directions are correct, then the line sums in every other direction can be corrected provided that the number of wrong line sums in that direction is less than k/2.

Three-Phase Well-Flow-Measurement and Well-Testing Unit Provides Accuracy, Agility

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper URTeC 3719030, “Not Measured, Not Improved: Agile Three-Phase Well-Flow-Measurement and Well-Testing Unit,” by Bali Singh and Bruce Gerrard, SPE, Apache, and David Reasoner, SPE, NeoTek Energy, et al. The paper has not been peer reviewed. _ The complete paper highlights well-test challenges, provides an overview of common problems, and describes the broader impact of inaccurate or infrequent well tests, with a focus on production testing of wells in the Permian Basin. Many of these challenges, however, apply to onshore oil and gas fields around the world. To overcome the measurement challenges in a cost-effective manner, the industry has taken multiple approaches to create various inline test devices with limited success. The authors introduce a measurement system that is agile for transport and can be installed anywhere with a small footprint while delivering reasonably accurate results. Introduction Measurement-system design included the following requirements: - Able to measure oil, water, and gas flow rates with reasonable accuracy - Agility allowing the system to be moved rapidly and easily by using a trailer behind a work truck - Installable and operational within 6 hours - Maximum 8×8-ft footprint - Must run standalone or in series with any other measurement system for validation testing - No requirement for additional infrastructure—capable of operation under its own power and communication with cellular or satellite phones and modems Theory and Methods Industry Practices: Importance of Accurate Well Tests. The standard test requirement for regulatory reporting in most provinces and states in North America is two 24-hour well tests per month. The 2 or more days of testing in a test separator, and the remaining days tested in a group separator, are used to estimate total monthly production volume allocated to the well. A sales meter is used to measure group production from a satellite for allocating revenues to the working-interest (WI) holders of each well or lease. In almost all fields, the production measured at the sales node does not match the combined production from multiple group lines that are run into the sales line. This poses a challenge because the sum of group lines is different from the volume measured by the sales meter. The challenge is addressed by prorating the difference between the sales meter and group lines back to the individual wells, called the proration factor. In the event of disagreement among WI owners, a large proration factor may cause custody-transfer issues. The good news is that the industry has developed many products used in specific applications to increase testing frequency and accuracy. The proposed measurement system fits well into this application and into much broader measurement categories. The measurement system was tested at Apache with highly favorable results and is ready to be deployed to optimize production allocation, well-test accuracy, and metering accuracy.

Low-level complex mosaic with multiple cell lines affecting the 18q21.31q21.32 region in a patient with de novo 18q terminal deletion

We describe a 5-year-old girl who was diagnosed at birth with 18q de novo homogeneous deletion at G-banding karyotype. Her clinical condition, characterized by hypotonia, psychomotor retardation, short stature, deafness secondary to bilateral atresia of the external auditory canals, was in agreement with the 18q deletion syndrome though presence of coloboma of a single eye only suggested a mosaic condition as an unusual sign. By combining multiple technologies including array-CGH, FISH, and WGS, we found that the terminal deletion 18q21.32q23 (21 Mb) was in segmental mosaicism of the proximal region 18q21.31q21.32 (2.7 Mb), which showed a variable number of copies: one, two, or three, in 7, 41 and 55% of the cells respectively. Breakpoint junction analysis demonstrated the presence of an inv-dup del (18q) with a disomic segment of 4.7 kb between the inverted and non-inverted copies of the duplicated region 18q21.31q21.32. From these results, we propose that all three types of abnormal chr18 (the inv-dup del and the two 18q terminal deletions of different sizes) arisen from breaks in a dicentric mirror chromosome 18q, either in more than one embryo cell or from subsequent breaking-fusion-bridge cycles. The duplication region was with identical polymorphisms as in all non-recurrent inv-dup del rearrangements though, in contrast with most of them, the 18q abnormality was of maternal origin. Taking into account that distal 18q deletions are not rarely associated with inv-dup del(18q) cell lines, and that the non-disjunction of chromosome 18 takes place especially at maternal meiosis II rather than meiosis I, multiple rescue events starting from trisomic zygotes could be considered alternative to the postmitotic ones. From the clinical point of view, our case, as well as those of del(18q) in mosaic with the dic(18q), shows that the final phenotype is the sum of the different cell lines that acted on embryonic development with signs typical of both the 18q deletion syndrome and trisomy 18. Asymmetrical malformations, such as coloboma of the iris only in the right eye, confirm the underlying mosaicism regardless of whether it is still detectable in the blood.

Ideal free dispersal in integrodifference models.

In this paper, we use an integrodifference equation model and pairwise invasion analysis to find what dispersal strategies are evolutionarily stable strategies (also known as evolutionarily steady or ESS) when there is spatial heterogeneity and possibly seasonal variation in habitat suitability. In that case there are both advantages and disadvantages of dispersing. We begin with the case where all spatial locations can support a viable population, and then consider the case where there are non-viable regions in the habitat. If the viable regions vary seasonally, and the viable regions in summer and winter do not overlap, dispersal may really be necessary for sustaining a population. Our findings generally align with previous findings in the literature that were based on other modeling frameworks, namely that dispersal strategies associated with ideal free distributions are evolutionarily stable. In the case where only part of the habitat can sustain a population, we show that a partial occupation ideal free distribution that occupies only the viable region is associated with a dispersal strategy that is evolutionarily stable. As in some previous works, the proofs of these results make use of properties of line sum symmetric functions, which are analogous to those of line sum symmetric matrices but applied to integral operators.

Number Cubes with Consecutive Line Sums

We settle the existence of certain “anti-magic” cubes using combinatorial block designs and graph decompositions to align a handful of small examples.

Abelian group actions and hypersmooth equivalence relations

We show that a Borel action of a standard Borel group which is isomorphic to a sum of a countable abelian group with a countable sum of real lines and circles induces an orbit equivalence relation which is hypersmooth, i.e., Borel reducible to eventual agreement on sequences of reals, and it follows from this result along with the structure theory for locally compact abelian groups that Borel actions of Polish LCA groups induce orbit equivalence relations which are essentially hyperfinite, extending a result of Gao and Jackson and answering a question of Ding and Gao.

Compensation for the variation of total number density to improve signal repeatability for laser-induced breakdown spectroscopy

High signal uncertainty has been regarded as a critical obstacle for the quantitative analysis of laser-induced breakdown spectroscopy (LIBS). One of the most effective ways for uncertainty reduction is to directly compensate for the variation of plasma properties, especially total number density. However, reliable compensation for the variation of total number density is hard to implement. In this work, we propose a data pre-processing method, called total number density compensation (TNDC), to reduce signal uncertainty. It is established on an assumption extended from the internal standard method and utilizes a weighted sum of emission lines from all major elements to reflect the variation of total number density. The TNDC method is tested on 29 brass samples and outperforms common normalization methods based on the spectral area in terms of signal repeatability and analytical performance. For Cu, the mean pulse-to-pulse relative standard deviation (RSD) of signals is greatly decreased from 5.10% to 1.03%, which is almost the best signal repeatability that LIBS can achieve and is comparable to that of ICP-OES. The root mean square error of prediction (RMSEP) and the mean RSD of prediction are decreased from 6.56% to 0.60% and from 12.00% to 1.03%, respectively. While for Zn, the mean RSD of signals improves from 6.43% to 4.12%, and the RMSEP is reduced from 1.57% to 0.59% with the RSD of prediction from 5.41% to 4.18%. Results demonstrate that TNDC can be an effective method for LIBS analysis especially for repeatability improvement.

Development of lidar for remote methane sensing using an optimal configuration of high-power laser diodes

A broadband differential absorption lidar (DIAL) is developed making us of the properties of high-power pulsed laser diodes for the purpose of monitoring methane, a major atmospheric greenhouse biogas. The detection range is optimized for the CH4 Q-branch 2v3 overtone spectrum centered at 1.667 μm and mixed with water-vapor absorption bands of. The resonance absorption evaluated of the DIAL signal is an integral sum of the multiple CH4 resonance absorption lines modulating the characteristic broad laser line and simultaneously compensating the interfering water-vapor absorption. A compact DIAL scheme is developed using an optimal configuration of high-power laser diodes matching the selected spectral parameters.

Substance P Antagonism as a Novel Therapeutic Option to Enhance Efficacy of Cisplatin in Triple Negative Breast Cancer and Protect PC12 Cells against Cisplatin-Induced Oxidative Stress and Apoptosis.

Simple SummaryAlthough cisplatin is very effective as a treatment strategy in triple-negative breast cancer (TNBC), it has unwarranted outcomes owing to recurrence, chemoresistance and neurotoxicity. In the current studies we determined a novel therapeutic option that enhances the efficacy of cisplatin and at the same time protects neuronal cells from cisplatin induced toxicity.Although cisplatin is very effective as a treatment strategy in triple-negative breast cancer (TNBC), it has unwarranted outcomes owing to recurrence, chemoresistance and neurotoxicity. There is critically important to find new, effective and safe therapeutics for TNBC. We determined if SP-receptor antagonism in combination with cisplatin may serve as a novel, more efficacious and safer therapeutic option than existing therapies for TNBC. We used a neuronal cell line (PC12) and two TNBC cell lines (Sum 185 and Sum 159) for these studies. We determined that the levels of cells expressing the high-affinity SP-receptor (neurokinin 1 receptor (NK1R)), as determined by flow-cytometry was significantly elevated in response to cisplatin in all three cells. We determined that treatment with aprepitant, an SP-receptor antagonist decreased cisplatin-induced, loss of viability (studied by MTT assay), production of reactive oxygen species (by DCFDA assay) and apoptosis (by flow-cytometry) in PC12 cells while it was increased in the two TNBC cells. Furthermore, we demonstrated that important genes associated with metastases, inflammation, chemoresistance and cell cycle progression are attenuated by SP-receptor antagonism in the TNBC cell line, Sum 185. These studies implicate that SP-receptor antagonism in combination with cisplatin may possibly serve as a novel, more efficacious and safer therapeutic option than existing therapies for TNBC.

Uniform and monotone line sum optimization

The line sum optimization problem asks for a (0,1)-matrix minimizing the sum of given functions evaluated at its row and column sums. We show that the uniform problem, with identical row functions and identical column functions, and the monotone problem, over matrices with nonincreasing row and column sums, are polynomial time solvable.

Algorithms for linear time reconstruction by discrete tomography II

The reconstruction of an unknown function f from its line sums is the aim of discrete tomography. However, two main aspects prevent reconstruction from being an easy task. In general, many solutions are allowed due to the presence of the switching functions. Even when uniqueness conditions are available, results about the NP-hardness of reconstruction algorithms make their implementation inefficient when the values of f are in certain sets. We show that this is not the case when f takes values in a field or a unique factorization domain, such as R or Z. We present a linear time reconstruction algorithm (in the number of directions and in the size of the grid), which outputs the original function values for all points outside of the switching domains. Freely chosen values are assigned to the other points, namely, those with ambiguities. Examples are provided.

Daily and annual shell growth in a long-lived freshwater bivalve as a proxy for winter snowpack

To assess the potential of long-lived freshwater bivalve shells as a proxy for river environments, we examined daily and annual growth increments and analysed trace elements in the shells of Margaritifera laevis collected alive from the Shiribetsu River, located in the central western region of Hokkaido, Japan. The sum of the daily growth lines within a single annual increment corresponded to the days when the average daily water temperature was greater than 9 °C, suggesting that shell deposition occurred from spring to autumn. The growing degree days (GDD) are correlated with the maximum snow depth in winter and the average river discharge in spring. We conducted trace element microanalysis across daily and annual growth increments by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and compared the results with in situ environmental data. Sharp peaks in the barium/calcium ratio (Ba/Ca) observed during spring river discharge also suggest that the growth of Margaritifera shells is influenced by winter snow volume and meltwater. A 67-year profile of the standard growth index (SGI) estimated from twelve individual annual growth histories correlates to the annual snowfall accumulation. Distinct decadal variability is observed in the SGI and synchronized with the North Pacific Index and Pacific Decadal Oscillation. Sclerochronological approaches using Margaritifera shells could be valuable for reconstructing river and atmospheric conditions during the winter season, which is influenced by the Asian winter monsoon in the central Hokkaido region.

On line sum optimization

We show that the column sum optimization problem, of finding a (0,1)-matrix with prescribed row sums which minimizes the sum of evaluations of given functions at its column sums, can be solved in polynomial time, either when all functions are the same or when all row sums are bounded by any constant. We conjecture that the more general line sum optimization problem, of finding a matrix minimizing the sum of given functions evaluated at its row sums and column sums, can also be solved in polynomial time.

Prognostic Value of Pretreatment Albumin-to-Alkaline Phosphatase Ratio in Extensive-Disease Small-Cell Lung Cancer: A Retrospective Cohort Study.

PurposeEvidence regarding the relationship between albumin-to-alkaline phosphatase ratio (AAPR) and overall survival (OS) in extensive-disease small-cell lung cancer (ED-SCLC) patients is limited. This study aimed to investigate whether AAPR was independently related to OS in ED-SCLC patients after adjusting for potential covariates.Patients and MethodsThis was a retrospective cohort study of 224 patients with ED-SCLC. The target independent and dependent variables were pretreatment AAPR and OS, respectively. Covariates included age; sex; Eastern Cooperative Oncology performance status score; smoking history; existence of metastasis to organs such as the bone, lung, liver, brain, malignant plural effusion and others; sum of organ metastasis (≤3, >3), evaluation of first-line treatment; and sum of treatment lines (<2, ≥2). Student’s t test or chi-squared test was used to analyze the associations between AAPR and clinical characteristics. Kaplan–Meier survival analysis and Cox’s proportional hazards regression model were used to assess the prognostic value of AAPR for OS.ResultsThe average patient age was 60.51±8.73 years, and 87.95% were men. A non-linear relationship between AAPR and OS was detected, with an inflection point of 0.35. The hazard ratios (HRs) of the left (AAPR <0.35) and right sides (AAPR ≥0.35) of inflection point were 0.04 (95% CI=0.00–0.70, p=0.0268) and 0.52 (95% CI=0.16–1.64, p=0.2659), respectively. Kaplan–Meier analysis showed a median OS of 9.73 months (95% CI=8.6–12.33) for AAPR <0.35 and 13.7 months (95% CI=11.43–16.37) for AAPR ≥0.35 (log-rank p<0.0001). The Cox proportional hazards model showed that AAPR <0.35 increased the risk of death after adjusting for potential confounders (HR=1.65, 95% CI=1.11–2.46). In subgroup analysis, the trends of HRs were increased across all subgroups with AAPR <0.35 after stratification.ConclusionPretreatment AAPR might be served as an independent prognostic indicator in ED-SCLC patients. Our findings should be further validated in large-scale and prospective clinical trials.