69 research outputs found
On the reconstruction of planar lattice-convex sets from the covariogram
A finite subset of is said to be lattice-convex if is
the intersection of with a convex set. The covariogram of
is the function associating to each u \in
\integer^d the cardinality of . Daurat, G\'erard, and Nivat and
independently Gardner, Gronchi, and Zong raised the problem on the
reconstruction of lattice-convex sets from . We provide a partial
positive answer to this problem by showing that for and under mild extra
assumptions, determines up to translations and reflections. As a
complement to the theorem on reconstruction we also extend the known
counterexamples (i.e., planar lattice-convex sets which are not
reconstructible, up to translations and reflections) to an infinite family of
counterexamples.Comment: accepted in Discrete and Computational Geometr
Approximation of corner polyhedra with families of intersection cuts
We study the problem of approximating the corner polyhedron using
intersection cuts derived from families of lattice-free sets in .
In particular, we look at the problem of characterizing families that
approximate the corner polyhedron up to a constant factor, which depends only
on and not the data or dimension of the corner polyhedron. The literature
already contains several results in this direction. In this paper, we use the
maximum number of facets of lattice-free sets in a family as a measure of its
complexity and precisely characterize the level of complexity of a family
required for constant factor approximations. As one of the main results, we
show that, for each natural number , a corner polyhedron with basic
integer variables and an arbitrary number of continuous non-basic variables is
approximated up to a constant factor by intersection cuts from lattice-free
sets with at most facets if and that no such approximation is
possible if . When the approximation factor is allowed to
depend on the denominator of the fractional vertex of the linear relaxation of
the corner polyhedron, we show that the threshold is versus .
The tools introduced for proving such results are of independent interest for
studying intersection cuts
Centerpoints: a link between optimization and convex geometry
We introduce a concept that generalizes several different notions of a “centerpoint” in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are “best possible” in a certain sense. Motivated by this, we establish several structural results about this concept and provide efficient algorithms for computing these points
Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma
Equations describing the linear evolution of a non-dissipative Langmuir wave
in inhomogeneous nonstationary anisotropic plasma without magnetic field are
derived in the geometrical optics approximation. A continuity equation is
obtained for the wave action density, and the conditions for the action
conservation are formulated. In homogeneous plasma, the wave field E
universally scales with the electron density N as E ~ N^{3/4}, whereas the
wavevector evolution varies depending on the wave geometry
Parametric Polyhedra with at least Lattice Points: Their Semigroup Structure and the k-Frobenius Problem
Given an integral matrix , the well-studied affine semigroup
\mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\} can be
stratified by the number of lattice points inside the parametric polyhedra
. Such families of parametric polyhedra appear in
many areas of combinatorics, convex geometry, algebra and number theory. The
key themes of this paper are: (1) A structure theory that characterizes
precisely the subset \mbox{ Sg}_{\geq k}(A) of all vectors b \in \mbox{
Sg}(A) such that has at least solutions. We
demonstrate that this set is finitely generated, it is a union of translated
copies of a semigroup which can be computed explicitly via Hilbert bases
computations. Related results can be derived for those right-hand-side vectors
for which has exactly solutions or fewer
than solutions. (2) A computational complexity theory. We show that, when
, are fixed natural numbers, one can compute in polynomial time an
encoding of \mbox{ Sg}_{\geq k}(A) as a multivariate generating function,
using a short sum of rational functions. As a consequence, one can identify all
right-hand-side vectors of bounded norm that have at least solutions. (3)
Applications and computation for the -Frobenius numbers. Using Generating
functions we prove that for fixed the -Frobenius number can be
computed in polynomial time. This generalizes a well-known result for by
R. Kannan. Using some adaptation of dynamic programming we show some practical
computations of -Frobenius numbers and their relatives
Derivatives of 9-phosphorylated acridine as butyrylcholinesterase inhibitors with antioxidant activity and the ability to inhibit β-amyloid self-aggregation: potential therapeutic agents for Alzheimer’s disease
We investigated the inhibitory activities of novel 9-phosphoryl-9,10-dihydroacridines and 9-phosphorylacridines against acetylcholinesterase (AChE), butyrylcholinesterase (BChE), and carboxylesterase (CES). We also studied the abilities of the new compounds to interfere with the self-aggregation of β-amyloid (Aβ42) in the thioflavin test as well as their antioxidant activities in the ABTS and FRAP assays. We used molecular docking, molecular dynamics simulations, and quantum-chemical calculations to explain experimental results. All new compounds weakly inhibited AChE and off-target CES. Dihydroacridines with aryl substituents in the phosphoryl moiety inhibited BChE; the most active were the dibenzyloxy derivative 1d and its diphenethyl bioisostere 1e (IC50 = 2.90 ± 0.23 µM and 3.22 ± 0.25 µM, respectively). Only one acridine, 2d, an analog of dihydroacridine, 1d, was an effective BChE inhibitor (IC50 = 6.90 ± 0.55 μM), consistent with docking results. Dihydroacridines inhibited Aβ42 self-aggregation; 1d and 1e were the most active (58.9% ± 4.7% and 46.9% ± 4.2%, respectively). All dihydroacridines 1 demonstrated high ABTS•+-scavenging and iron-reducing activities comparable to Trolox, but acridines 2 were almost inactive. Observed features were well explained by quantum-chemical calculations. ADMET parameters calculated for all compounds predicted favorable intestinal absorption, good blood–brain barrier permeability, and low cardiac toxicity. Overall, the best results were obtained for two dihydroacridine derivatives 1d and 1e with dibenzyloxy and diphenethyl substituents in the phosphoryl moiety. These compounds displayed high inhibition of BChE activity and Aβ42 self-aggregation, high antioxidant activity, and favorable predicted ADMET profiles. Therefore, we consider 1d and 1e as lead compounds for further in-depth studies as potential anti-AD preparations
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Antithrombotic therapy after acute coronary syndrome or PCI in atrial fibrillation
BACKGROUND: Appropriate antithrombotic regimens for patients with atrial fibrillation who have an acute coronary syndrome or have undergone percutaneous coronary intervention (PCI) are unclear. METHODS: In an international trial with a two-by-two factorial design, we randomly assigned patients with atrial fibrillation who had an acute coronary syndrome or had undergone PCI and were planning to take a P2Y12 inhibitor to receive apixaban or a vitamin K antagonist and to receive aspirin or matching placebo for 6 months. The primary outcome was major or clinically relevant nonmajor bleeding. Secondary outcomes included death or hospitalization and a composite of ischemic events. RESULTS: Enrollment included 4614 patients from 33 countries. There were no significant interactions between the two randomization factors on the primary or secondary outcomes. Major or clinically relevant nonmajor bleeding was noted in 10.5% of the patients receiving apixaban, as compared with 14.7% of those receiving a vitamin K antagonist (hazard ratio, 0.69; 95% confidence interval [CI], 0.58 to 0.81; P<0.001 for both noninferiority and superiority), and in 16.1% of the patients receiving aspirin, as compared with 9.0% of those receiving placebo (hazard ratio, 1.89; 95% CI, 1.59 to 2.24; P<0.001). Patients in the apixaban group had a lower incidence of death or hospitalization than those in the vitamin K antagonist group (23.5% vs. 27.4%; hazard ratio, 0.83; 95% CI, 0.74 to 0.93; P = 0.002) and a similar incidence of ischemic events. Patients in the aspirin group had an incidence of death or hospitalization and of ischemic events that was similar to that in the placebo group. CONCLUSIONS: In patients with atrial fibrillation and a recent acute coronary syndrome or PCI treated with a P2Y12 inhibitor, an antithrombotic regimen that included apixaban, without aspirin, resulted in less bleeding and fewer hospitalizations without significant differences in the incidence of ischemic events than regimens that included a vitamin K antagonist, aspirin, or both. (Funded by Bristol-Myers Squibb and Pfizer; AUGUSTUS ClinicalTrials.gov number, NCT02415400.)
Extended Thromboprophylaxis with Betrixaban in Acutely Ill Medical Patients
Background
Patients with acute medical illnesses are at prolonged risk for venous thrombosis. However, the appropriate duration of thromboprophylaxis remains unknown.
Methods
Patients who were hospitalized for acute medical illnesses were randomly assigned to receive subcutaneous enoxaparin (at a dose of 40 mg once daily) for 10±4 days plus oral betrixaban placebo for 35 to 42 days or subcutaneous enoxaparin placebo for 10±4 days plus oral betrixaban (at a dose of 80 mg once daily) for 35 to 42 days. We performed sequential analyses in three prespecified, progressively inclusive cohorts: patients with an elevated d-dimer level (cohort 1), patients with an elevated d-dimer level or an age of at least 75 years (cohort 2), and all the enrolled patients (overall population cohort). The statistical analysis plan specified that if the between-group difference in any analysis in this sequence was not significant, the other analyses would be considered exploratory. The primary efficacy outcome was a composite of asymptomatic proximal deep-vein thrombosis and symptomatic venous thromboembolism. The principal safety outcome was major bleeding.
Results
A total of 7513 patients underwent randomization. In cohort 1, the primary efficacy outcome occurred in 6.9% of patients receiving betrixaban and 8.5% receiving enoxaparin (relative risk in the betrixaban group, 0.81; 95% confidence interval [CI], 0.65 to 1.00; P=0.054). The rates were 5.6% and 7.1%, respectively (relative risk, 0.80; 95% CI, 0.66 to 0.98; P=0.03) in cohort 2 and 5.3% and 7.0% (relative risk, 0.76; 95% CI, 0.63 to 0.92; P=0.006) in the overall population. (The last two analyses were considered to be exploratory owing to the result in cohort 1.) In the overall population, major bleeding occurred in 0.7% of the betrixaban group and 0.6% of the enoxaparin group (relative risk, 1.19; 95% CI, 0.67 to 2.12; P=0.55).
Conclusions
Among acutely ill medical patients with an elevated d-dimer level, there was no significant difference between extended-duration betrixaban and a standard regimen of enoxaparin in the prespecified primary efficacy outcome. However, prespecified exploratory analyses provided evidence suggesting a benefit for betrixaban in the two larger cohorts. (Funded by Portola Pharmaceuticals; APEX ClinicalTrials.gov number, NCT01583218. opens in new tab.
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