Enumerative Combinatorics: Contents

While the intersection of the Grassmannian Bruhat decompositions for all coordinate flags is an intractable mess, it turns out that the intersection of only the cyclic shifts of one Bruhat decomposition has many of the good properties of the Bruhat and Richardson decompositions. This decomposition coincides with the projection of the Richardson stratification of the flag manifold, studied by Lusztig, Rietsch, Brown–Goodearl–Yakimov and the present authors. However, its cyclic-invariance is hidden in this description. Postnikov gave many cyclic-invariant ways to index the strata, and we give a new one, by a subset of the affine Weyl group we call bounded juggling patterns. We call the strata positroid varieties. Applying results from [A. Knutson, T. Lam and D. Speyer, Projections of Richardson varieties, J. Reine Angew. Math., to appear, arXiv:1008.3939 [math.AG]], we show that positroid varieties are normal, Cohen–Macaulay, have rational singularities, and are defined as schemes by the vanishing of Plucker coordinates. We prove that their associated cohomology classes are represented by affine Stanley functions. This latter fact lets us connect Postnikov’s and Buch–Kresch–Tamvakis’ approaches to quantum Schubert calculus.

/pdf/positroid-varieties-juggling-and-geometry-2fedcr4058.pdf

Positroid varieties: juggling and geometry

In wireless sensor networks (WSN), routing is quite challenging area of research where packets are forwarded through multiple nodes to the base station. The packet being sent over the network should be shared in an energy efficient manner. It also considers the residual power of battery to enhance the network life time. Existing energy efficient routing solutions and surveys are presented but still there is a need for Systematic Literature Review (SLR) to identify the valid problems. This paper performs SLR for energy efficiency routing with 172 papers at initial stage. Next, 50 papers are shortlisted after filtration based on quality valuation and selection criteria by ensuring relevance with energy efficiency. Initially, we present literature that includes schemes for threshold sensitive, adaptive periodic threshold sensitive, power efficient, hybrid energy efficient distribution and low energy adaptive mechanisms. Result of systematic review reveals that consumption of energy is the most fundamental issue in WSN however, is not noticed by the researchers and practitioners where as it can contribute for the improvement of the energy efficiency. It also elaborates the weaknesses of the existing approaches which make them inappropriate for energy efficient routing in WSN.

Systematic Literature Review on Energy Efficient Routing Schemes in WSN – A Survey

The Internet of Things (IoT) is gaining attention because of its broad applicability, especially by integrating smart devices for massive communication during sensing tasks. IoT-assisted Wireless Sensor Networks (WSN) are suitable for various applications like industrial monitoring, agriculture, and transportation. In this regard, routing is challenging to nd an ef cient path using smart devices for transmitting the packets towards big data repositories while ensuring ef cient energy utilization. This paper presents the Robust Cluster Based Routing Protocol (RCBRP) to identify the routing paths where less energy is consumed to enhances the network lifespan. The scheme is presented in six phases to explore ow and communication. We propose the two algorithms: i) energy-ef cient clustering and routing algorithm and ii) distance and energy consumption calculation algorithm. The scheme consumes less energy and balances the load by clustering the smart devices. Our work is validated through extensive simulation using Matlab. Results elucidate the dominance of the proposed scheme is compared to counterparts in terms of energy consumption, the number of packets received at BS and the number of active and dead nodes. In the future, we shall consider edge computing to analyze the performance of robust clustering.

Robust Cluster-Based Routing Protocol for IoT-Assisted Smart Devices in WSN

We derive closed form expressions and limiting formulae for a variety of functions of a permutation resulting from repeated riffle shuffles. The results allow new formulae and approximations for the number of permutations inS
 n with given cycle type and number of descents. The theorems are derived from a bijection discovered by Gessel. A self-contained proof of Gessel's result is given.

Riffle shuffles, cycles, and descents

Researchers in wireless sensor networks (WSN), have given deep attention to large scale integration and energy-efficiency (energy consumption) Energy-efficient solutions can conserve valuable sensor-node energy This is one of the main critical challenges that WSNs face, which plays a fundamental part in determining the lifetime of the network Although, there are many WSN protocols, clustering based hierarchal routing protocols are given more consideration because of their improve scalability In particular, sensors are battery-powered, often limiting available energy, which is not changeable in most of the situations One of the most common energy-efficiency sensor networks protocols is Low Energy Adaptive Clustering Hierarchy (LEACH) as source In this paper, we propose CH-leach We present architectures, schemes and evaluate Its performance using analytical study and simulations The evaluation was based on the most critical metrics in WSNs, such as: energy-efficiency (energy consumption), and network lifetime The evaluation and comparison with existing solutions show that our proposed CH-leach exhibits a reduction in energy consumption over LEACH and DEEC While the overall network lifetime of CH-leach is improved 91% and 43% more than LEACH and DEEC protocols respectively

An energy efficient and adaptive clustering for wireless sensor network (CH-leach) using leach protocol

As fuel costs continue to rise, efficient public transport, especially rail will play an increasingly important role in the UK and worldwide. For the safe operation of the rail system, it is necessary that the condition of the rails can be monitored on a continual basis. An important part of this monitoring process is crack detection. Much research effort has been spent in the development of reliable, repeatable crack detection methods for the use on the service rail. In this research a new crack detection method has been investigated which utilizes microwave sensors to inspect the rail surface. Initial data from experiment are presented.

http://iopscience.iop.org/article/10.1088/1742-6596/178/1/012033/pdf

Non invasive rail track detection system using microwave sensor

Low cost undulator magnets for industrial free electron masers

Electrostatic accelerator FEL oscillators when operated with energy recovery offer the prospect of long pulse, single-mode operation with very narrow linewidth at high-power levels. However, special care with wiggler construction, electron beam steering, and collector design is necessary to reduce the fraction of the electron beam lost before depressed collection to a sufficiently small value to stop the output hopping from one longitudinal mode of the cavity to another due to the droop of the terminal accelerating voltage. We are investigating what minimum recovery fraction is required both experimentally and theoretically. We have constructed a pulsed microwave FEM oscillator having an accelerating voltage of 65 kV supplied by a source, which is a capacitor, charged by a low-current, high-voltage supply. By changing the capacitor value, it is easily possible to achieve a range of voltage droop rates. Furthermore, because the gain bandwidth of the FEM is small, only 1 or 2 longitudinal modes are capable of being amplified at any voltage which eases the problem of analysing mode hopping behaviour. A simple model of mode switching is outlined.

The effect of voltage droop on the output of an electrostatic accelerator free electron laser

It has recently been proposed that a folded waveguide travelling wave tube could be constructed using silicon microfabrication technology. When configured as an oscillator this device could provide a high power (>100mW), highly efficient (>15%), reliable, compact and cheap source for the Terahertz Gap. This paper will present the current status of Liverpool John Moores University THz source. This will include theoretical and numerical simulations of the electron beam interaction with the electromagnetic waves (EM) and the design and construction of the EM wave interaction cavity. This research project is supported by the UK EMRS/DTC.

Compact Tuneable Terahertz Source

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

C.C. Wright

Author Tools

Chat about Author