Homology of perfect complexes

It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective dimension, obstructions to realizing R as a closed fiber of some flat local homomorphism. Other applications include, as special cases, uniform proofs of known results on free actions of elementary abelian groups and of tori on finite CW complexes. The arguments use numerical invariants of objects in general triangulated categories, introduced here and called levels. They allow one to track, through changes of triangulated categories, homological invariants like projective dimension, as well as structural invariants like Loewy length. An intermediate result sharpens, with a new proof, the New Intersection Theorem for commutative algebras over fields. Under additional hypotheses on the ring $R$ stronger estimates are proved for Loewy lengths of modules of finite projective dimension.Comment: This version corrects an error in the statement (and proof) of Theorem 7.4 in the published version of the paper [Adv. Math. 223 (2010) 1731--1781]. These changes do not affect any other results or proofs in the paper. A corrigendum has been submitted

Two-Hop Routing with Traffic-Differentiation for QoS Guarantee in Wireless Sensor Networks

This paper proposes a Traffic-Differentiated Two-Hop Routing protocol for Quality of Service (QoS) in Wireless Sensor Networks (WSNs). It targets WSN applications having different types of data traffic with several priorities. The protocol achieves to increase Packet Reception Ratio (PRR) and reduce end-to-end delay while considering multi-queue priority policy, two-hop neighborhood information, link reliability and power efficiency. The protocol is modular and utilizes effective methods for estimating the link metrics. Numerical results show that the proposed protocol is a feasible solution to addresses QoS service differenti- ation for traffic with different priorities.Comment: 13 page

A New Method of Image Compression Using Irreducible Covers of Maximal Rectangles

In recent years there has been a tremendous spurt in research and activity in finding efficient compression techniques for image processing applications. Particularly when an image is structured over a non-rectangular region it is always advantageous to define a method of covering a region by minimal numbers of maximal rectangles. Towards this objective, we analyze the binary image compression problem using irreducible cover of maximal rectangles. We also give a bound on the minimum rectangular cover problem for image compression under certain conditions that previously have not been analyzed. It is demonstrated for a simply connected image that, the irreducible cover proposed here uses less than four times the number of the rectangles in a minimum cover. With n pixels in a square, the parallel algorithm of obtaining the irreducible cover presented in the paper uses (n/log n) concurrent-read-exclusive-write (CREW) processors in O(log n) time

Forecasting Stock Time-Series using Data Approximation and Pattern Sequence Similarity

Time series analysis is the process of building a model using statistical techniques to represent characteristics of time series data. Processing and forecasting huge time series data is a challenging task. This paper presents Approximation and Prediction of Stock Time-series data (APST), which is a two step approach to predict the direction of change of stock price indices. First, performs data approximation by using the technique called Multilevel Segment Mean (MSM). In second phase, prediction is performed for the approximated data using Euclidian distance and Nearest-Neighbour technique. The computational cost of data approximation is O(n ni) and computational cost of prediction task is O(m |NN|). Thus, the accuracy and the time required for prediction in the proposed method is comparatively efficient than the existing Label Based Forecasting (LBF) method [1].Comment: 11 page

The stochastic modelling of kleptoparasitism using a Markov process

Kleptoparasitism, the stealing of food items from other animals, is a common behaviour observed across a huge variety of species, and has been subjected to significant modelling effort. Most such modelling has been deterministic, effectively assuming an infinite population, although recently some important stochastic models have been developed. In particular the model of Yates and Broom (Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480–489) introduced a stochastic version following the original model of Ruxton and Moody (The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449–458), and whilst they generated results of interest, they did not solve the model explicitly. In this paper, building on methods used already by van der Meer and Smallegange (A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134–142) we give an exact solution to the distribution of the population over the states for the Yates and Broom model and investigate the effects of some key biological parameters, especially for small populations where stochastic models can be expected to differ most from their deterministic equivalents

Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy non-stationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an {\it a-priori} known scaling exponent $\alpha_{0}$ and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent $\alpha_{0}$, and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.Comment: 15 pages, 16 figure

Comets, historical records and vedic literature

A verse in book I of Rigveda mentions a cosmic tree with rope-like aerial roots held up in the sky. Such an imagery might have ensued from the appearance of a comet having `tree stem' like tail, with branched out portions resembling aerial roots. Interestingly enough, a comet referred to as `heavenly tree' was seen in 162 BC, as reported by old Chinese records. Because of weak surface gravity, cometary appendages may possibly assume strange shapes depending on factors like rotation, structure and composition of the comet as well as solar wind pattern. Varahamihira and Ballala Sena listed several comets having strange forms as reported originally by ancient seers such as Parashara, Vriddha Garga, Narada and Garga. Mahabharata speaks of a mortal king Nahusha who ruled the heavens when Indra, king of gods, went into hiding. Nahusha became luminous and egoistic after absorbing radiance from gods and seers. When he kicked Agastya (southern star Canopus), the latter cursed him to become a serpent and fall from the sky. We posit arguments to surmise that this Mahabharata lore is a mythical recounting of a cometary event wherein a comet crossed Ursa Major, moved southwards with an elongated tail in the direction of Canopus and eventually went out of sight. In order to check whether such a conjecture is feasible, a preliminary list of comets (that could have or did come close to Canopus) drawn from various historical records is presented and discussed.Comment: This work was presented in the International Conference on Oriental Astronomy held at IISER, Pune (India) during November, 201

Framing and Immigration Through the Trump Era

For the last decade, undocumented or illegal immigration has been one of the most contested policy issues in the United States, with significant news attention on policies affecting the undocumented population, ranging from deportations to comprehensive immigration reform, the DREAM Act, and Deferred Action for Childhood Arrivals. Despite these prominent and multifaceted policy debates, scholarship on media framing and public opinion remain more focused on the portrayal of immigrants rather than policies affecting them. In general, we find that policy frames are far more consequential to public opinion than equivalency frames (variations in how news media describe unauthorized immigrants, either as illegal or undocumented ) or episodic frames (whether news articles are heavy on human-interest stories rather than policy facts and statistics). In addition, negative frames generally have stronger effects than positive frames, and these effects sometimes vary by partisanship and family migration history. Finally, the relative infrequency of powerful frames in news stories, like time spent living in the United States, provides opportunities for advocates to move public opinion on immigration policy. These findings have important implications for future battles over immigration policy in the United States, which show no signs of abating