Curvature estimates for submanifolds in warped products

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.Comment: 21 page

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form $\Theta(n^k)$, for some integer $k\leq d$, where $d$ is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal $k$. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a $k$ such that the termination complexity is $\Omega(n^k)$. Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925

Stability improvement of an efficient graphene nanoribbon field-effect transistor-based sram design

The development of the nanoelectronics semiconductor devices leads to the shrinking of transistors channel into nanometer dimension. However, there are obstacles that appear with downscaling of the transistors primarily various short-channel effects. Graphene nanoribbon field-effect transistor (GNRFET) is an emerging technology that can potentially solve the issues of the conventional planar MOSFET imposed by quantum mechanical (QM) effects. GNRFET can also be used as static random-access memory (SRAM) circuit design due to its remarkable electronic properties. For high-speed operation, SRAM cells are more reliable and faster to be effectively utilized as memory cache. The transistor sizing constraint affects conventional 6T SRAM in a trade-off in access and write stability. This paper investigates on the stability performance in retention, access, and write mode of 15 nm GNRFET-based 6T and 8T SRAM cells with that of 16 nm FinFET and 16 nm MOSFET. The design and simulation of the SRAM model are simulated in synopsys HSPICE. GNRFET, FinFET, and MOSFET 8T SRAM cells give better performance in static noise margin (SNM) and power consumption than 6T SRAM cells. The simulation results reveal that the GNRFET, FinFET, and MOSFET-based 8T SRAM cells improved access static noise margin considerably by 58.1%, 28%, and 20.5%, respectively, as well as average power consumption significantly by 97.27%, 99.05%, and 83.3%, respectively, to the GNRFET, FinFET, and MOSFET-based 6T SRAM design. © 2020 Mathan Natarajamoorthy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Protective role of Withaferin-a on red blood cell integrity during 7,12-dimethylbenz[A]anthracene induced oral carcinogenesis

The aim of the present study was to investigate the protective effect of Withaferin-A on red blood cell integrity during 7,12-dimethylbenz[a]anthracene (DMBA) induced oral carcinogenesis. The protective effect of Withaferin-A was assessed by measuring the status of glycoconjugates, membrane bound enzyme activity and red blood cell osmotic fragility. Oral squamous cell carcinoma was induced in the buccal pouch of Syrian golden hamsters by painting with 0.5% DMBA in liquid paraffin thrice a week for 14 weeks. The levels of glycoconjugates, membrane bound enzyme activity, osmotic fragility and thiobarbituric acid reactive substances (TBARS) were analyzed by using specific colorimetric methods. We observed 100% tumor formation in DMBA painted hamsters. Increase in plasma glycoconjugates at the expense of red blood cell membrane glycoconjugates levels were observed in DMBA painted hamsters as compared to control hamsters. Erythrocytes from DMBA painted hamsters were more fragile than those from control hamsters. The activity of membrane bound enzyme (Na+ K+ ATPase) decreased whereas TBARS level was increased in DMBA painted hamsters as compared to control hamsters. Oral administration of Withaferin-A at a dose of 20mg kg-1 bw significantly prevented the tumor formation as well as normalized the biochemical variables in DMBA painted hamsters. Our results thus demonstrate the protective effect of Withaferin-A on red blood cell integrity during DMBA induced oral carcinogenesis.Key words: DMBA, Withaferin-A, Oral cancer, glycoconjugates, osmotic fragility

Space-times which are asymptotic to certain Friedman-Robertson-Walker space-times at timelike infinity

We define space-times which are asymptotic to radiation dominant Friedman-Robertson-Walker space-times at timelike infinity and study the asymptotic structure. We discuss the local asymptotic symmetry and give a definition of the total energy from the electric part of the Weyl tensor.Comment: 8 pages, Revte

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201