Approximating the Maximum Overlap of Polygons under Translation

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which maximizes its area of overlap with $P$. Our algorithm runs in $O(c n)$ time, where $c$ is a constant that depends only on $k$ and $\varepsilon$. This suggest that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time

System multilayered applied to the radiative cooling

In applied optics, the multilayered structures (MLS) take an important place in many instrumental and industrial devices. The aim of this work is to study the MLS in order to optimize the inverse greenhouse effect; it is made by a survey on theoretical formalism of the energy exchange phenomena. This optimization requires that the window materials (MLS) are good reflectors in the visible range and assuring a total transmission in the infrared zone (8-13 µm); One of the support elements, of the window, answering to these criterions is germanium, for which we have studied the thickness influence and have found that the equilibrium temperature reached by the absorber has a minimal value between 0.01 µm and 0.06 µm. However, only with germanium, the window can not products the inverse greenhouse effect. Indeed, the germanium must include other layers in order to increase the visible reflectance and the infrared transmittance (8-13µm); what forms a multilayered structure. Several system have been used, only 7 of them have been kept for this work: S1, S2, …, S7 systems. Only the following systems: S2/S1, S3/S2/S1 and MgO/S3/S2/S1 give a radiative cooling effect, with a very good result of 15 °C below ambient temperature in the case of the S6 system. To approach of the real conditions of this system realization (S6), we simulated the effects of such imperfections, as presence of air, that would be due to the quality of the layers deposition. This study is made in the case of the S7 system. As results, we found that, for zenithal angles ≤ 60°, the layers of air, for which the thickness is lower than 0.5 µm, don't present any influence on the absorber's equilibrium temperature.In applied optics, the multilayered structures (MLS) take an important place in many instrumental and industrial devices. The aim of this work is to study the MLS in order to optimize the inverse greenhouse effect; it is made by a survey on theoretical formalism of the energy exchange phenomena. This optimization requires that the window materials (MLS) are good reflectors in the visible range and assuring a total transmission in the infrared zone (8-13 µm); One of the support elements, of the window, answering to these criterions is germanium, for which we have studied the thickness influence and have found that the equilibrium temperature reached by the absorber has a minimal value between 0.01 µm and 0.06 µm. However, only with germanium, the window can not products the inverse greenhouse effect. Indeed, the germanium must include other layers in order to increase the visible reflectance and the infrared transmittance (8-13µm); what forms a multilayered structure. Several system have been used, only 7 of them have been kept for this work: S1, S2, …, S7 systems. Only the following systems: S2/S1, S3/S2/S1 and MgO/S3/S2/S1 give a radiative cooling effect, with a very good result of 15 °C below ambient temperature in the case of the S6 system. To approach of the real conditions of this system realization (S6), we simulated the effects of such imperfections, as presence of air, that would be due to the quality of the layers deposition. This study is made in the case of the S7 system. As results, we found that, for zenithal angles ≤ 60°, the layers of air, for which the thickness is lower than 0.5 µm, don't present any influence on the absorber's equilibrium temperature

Microstructure Bio-Material for Behavioral Analysis

Biological applications have a limitation of creating tissue like structures in order to mimic the advanced real like structures, such as human tissues in a small scale. Conventional methods of using lab mice for cancer behavior have limitations due to observation complications. Fabricating an artificial human tissue which can behave similar to a human body tissue consists of components, such as Laminin and Collagen. Collagen in human tissue has elements, such as integrin and serum. Creating serum based proteins are somewhat challenging due to the conditional requirements. This particular approach will address the primary state of the art technique of observing the interaction with cells by mimicking the organs on a chip with blood circulation using a micro-fluidic pump. Bio-material hydrogel structures implanted on a silicon polymer based chip described in this thesis will overcome the limitations of in-vitro analysis. Water purification has become a vital issue in developing countries of the world. Water pollution due to Ammonia has been one of the major concerns with industrial revolution. Purifications were mainly done by chemical methods that can cause human health concerns. The analytically demonstrated method in this thesis using bio-compatible hydrogel will address a new dimension to the water conservation method without causing health issues and eliminating the environmental pollution due to complicated degradable structures. Filtration and efficiency are among the main concerns of using bacteria types such as AOB/NOB directly without encapsulating. Application of using bio-compatible hydrogel based dual encapsulated single pallet structure described in this thesis will address the issue of filtering capability. Pallets can be removed once nitrified, without letting it grow inside the water contaminating aqua based living breads and plants. The process will improve the efficiency of Ammonia removal due to encapsulation. Drug delivery using micro locomotives in neuro-surgery has become one of the future concerns with the development of science. Conventional delivery systems such as vaccines and open surgeries take longer response time once surgeries become more complex. Moreover there is a risk factor of injuring healthy nerves in the organ. Drug delivery approaches of drug encapsulated microspheres and drug embedded nematodes described in this thesis become more applicable to complex scenarios. Nematodes become useful in the future of microsurgeries, as many biologists are focusing on using their healthy nerves to implant in humans. Therefore, such applications like magnetizing nematodes help move locomotives to targeted locations and capture scan images for future medical approaches

Affine convex body semigroups

In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroup of [7]. Several properties of these semigroups are proven. Affine convex body semigroups obtained from circles and polygons of R^2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them

Hyperpolarized 13C-pyruvate MRI detects real-time metabolic flux in prostate cancer metastases to bone and liver: a clinical feasibility study.

BackgroundHyperpolarized (HP) 13C-pyruvate MRI is a stable-isotope molecular imaging modality that provides real-time assessment of the rate of metabolism through glycolytic pathways in human prostate cancer. Heretofore this imaging modality has been successfully utilized in prostate cancer only in localized disease. This pilot clinical study investigated the feasibility and imaging performance of HP 13C-pyruvate MR metabolic imaging in prostate cancer patients with metastases to the bone and/or viscera.MethodsSix patients who had metastatic castration-resistant prostate cancer were recruited. Carbon-13 MR examination were conducted on a clinical 3T MRI following injection of 250 mM hyperpolarized 13C-pyruvate, where pyruvate-to-lactate conversion rate (kPL) was calculated. Paired metastatic tumor biopsy was performed with histopathological and RNA-seq analyses.ResultsWe observed a high rate of glycolytic metabolism in prostate cancer metastases, with a mean kPL value of 0.020 ± 0.006 (s-1) and 0.026 ± 0.000 (s-1) in bone (N = 4) and liver (N = 2) metastases, respectively. Overall, high kPL showed concordance with biopsy-confirmed high-grade prostate cancer including neuroendocrine differentiation in one case. Interval decrease of kPL from 0.026 at baseline to 0.015 (s-1) was observed in a liver metastasis 2 months after the initiation of taxane plus platinum chemotherapy. RNA-seq found higher levels of the lactate dehydrogenase isoform A (Ldha,15.7 ± 0.7) expression relative to the dominant isoform of pyruvate dehydrogenase (Pdha1, 12.8 ± 0.9).ConclusionsHP 13C-pyruvate MRI can detect real-time glycolytic metabolism within prostate cancer metastases, and can measure changes in quantitative kPL values following treatment response at early time points. This first feasibility study supports future clinical studies of HP 13C-pyruvate MRI in the setting of advanced prostate cancer

Elevated Tumor Lactate and Efflux in High-grade Prostate Cancer demonstrated by Hyperpolarized 13C Magnetic Resonance Spectroscopy of Prostate Tissue Slice Cultures.

Non-invasive assessment of the biological aggressiveness of prostate cancer (PCa) is needed for men with localized disease. Hyperpolarized (HP) 13C magnetic resonance (MR) spectroscopy is a powerful approach to image metabolism, specifically the conversion of HP [1-13C]pyruvate to [1-13C]lactate, catalyzed by lactate dehydrogenase (LDH). Significant increase in tumor lactate was measured in high-grade PCa relative to benign and low-grade cancer, suggesting that HP 13C MR could distinguish low-risk (Gleason score ≤3 + 4) from high-risk (Gleason score ≥4 + 3) PCa. To test this and the ability of HP 13C MR to detect these metabolic changes, we cultured prostate tissues in an MR-compatible bioreactor under continuous perfusion. 31P spectra demonstrated good viability and dynamic HP 13C-pyruvate MR demonstrated that high-grade PCa had significantly increased lactate efflux compared to low-grade PCa and benign prostate tissue. These metabolic differences are attributed to significantly increased LDHA expression and LDH activity, as well as significantly increased monocarboxylate transporter 4 (MCT4) expression in high- versus low- grade PCa. Moreover, lactate efflux, LDH activity, and MCT4 expression were not different between low-grade PCa and benign prostate tissues, indicating that these metabolic alterations are specific for high-grade disease. These distinctive metabolic alterations can be used to differentiate high-grade PCa from low-grade PCa and benign prostate tissues using clinically translatable HP [1-13C]pyruvate MR