Fast MCMC sampling algorithms on polytopes

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya whereas the latter uses John's ellipsoids. We show that the Vaidya walk mixes in significantly fewer steps than the logarithmic-barrier based Dikin walk studied in past work. For a polytope in $\mathbb{R}^d$ defined by $n >d$ linear constraints, we show that the mixing time from a warm start is bounded as $\mathcal{O}(n^{0.5}d^{1.5})$, compared to the $\mathcal{O}(nd)$ mixing time bound for the Dikin walk. The cost of each step of the Vaidya walk is of the same order as the Dikin walk, and at most twice as large in terms of constant pre-factors. For the John walk, we prove an $\mathcal{O}(d^{2.5}\cdot\log^4(n/d))$ bound on its mixing time and conjecture that an improved variant of it could achieve a mixing time of $\mathcal{O}(d^2\cdot\text{polylog}(n/d))$. Additionally, we propose variants of the Vaidya and John walks that mix in polynomial time from a deterministic starting point. The speed-up of the Vaidya walk over the Dikin walk are illustrated in numerical examples.Comment: 86 pages, 9 figures, First two authors contributed equall

"गण्डावतरणम् कथाश्रित भारतीय-चिन्तन-परम्परा एवं उसके आलोक में कवि नीलकंठ दीक्षित विरचित गण्डावतरणम् महाकाव्य का समीक्षात्मक अध्ययन"

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Coarse wavelength division multiplexer on silicon-on-insulator for 100 GbE

A four-channel cascaded MZl based de-multiplexer at O-band with coarse channel spacing of 20 nm and band flatness of 13 nm is demonstrated on silicon-on-insulator. The device shows a mean crosstalk and insertion loss below -16 dB and 2.5 dB

Analysis of curtailment at The Geysers geothermal Field, California

Geothermal energy has traditionally been viewed as a baseload energy source, but the rapid growth of intermittent renewable energy has led to a need for more flexibility in power generation to avoid mandatory curtailment imposed by grid operators. This study of curtailment at The Geysers provides insights into the magnitude, duration, frequency, temporal and spatial distribution, and potential causes of curtailment events between 2013 and 2018. Annual levels of curtailment range during this period from 9 to 47 GW h, representing 0.15 to 0.81 % of the net generation. Most curtailments occurred at the power plants connected to a lower capacity transmission line and may result from transmission constriction. There is a clear link between negative pricing and economic curtailment, especially when solar production is higher. Economic curtailment events tend to be only a few hours and vary in magnitude up to almost 300 MW, whereas transmission-related curtailment events can be up to several weeks in duration. It is likely that curtailment of geothermal power will be an increasing concern, and could be mitigated by flexible generation strategies and increases in energy storage. It is critical to know the nature of curtailment events so that flexible generation options can be assessed properly

Does online retail coupons and memberships create favourable psychological disposition?

This study aims to examine the impact of coupons, portal membership and peer-influence on consumer purchase and psychological actions, which is built on the theory of impulsiveness and the theory of dissonance. The study uses 2x2x2 (i.e. coupons, peer influence, complimentary coupons) factorial experimental design to investigate the proposed hypothetical model. The experiment was conducted with 364 participants. The study used a two-step structural equation modelling analysis to validate the proposed hypothetical model. The findings suggest that an increase in coupons can positively enhance the purchase actions and impulsiveness, which can later influence cognitive post purchase dissonance (CPPD) and affective post-purchase dissonance (APPD), as well as customers repurchase intention. It was also found that providing additional complimentary coupons reduces the effect of CPPD but not of the APPD. This study contributes to dissonance theory by adding APPD into the framework; moreover, the results on the coupons, memberships and peer influence will offer further insights to practitioners

Nature of genetic control of the length and number of elongated internodes in deepwater rice under non-flooded condition

Inheritance of total length and number of elongated internodes in some varities of deepwater rice were studied in a 7 X 7 diallel (excluding reciprocals) by a procedure that does not require flooding. Estimates of combining ability and genetic component analysis showed highly significant additive and non-additive gene effects with preponderance of additive type. The high estimate of narrow sense heritability further supported the importance of additive gene effects. lalmagna and IR40905-11-3-1-5-2-21 were not always the best combiners. The significance of the gene distribution indicated the presence of gene asymmetry. The average degree of dominance was 8.83 for both total length and number of elongated internodes indicating partial dominance

Utilization of Nano Technology in Reducing Moisture Content of Phosphate Cake at RSMML Rock Phosphate Beneficiation Plant

After the induction of High Pressure Grinding Rolls at rock Phosphate Beneficiation Plant, The belt Drum Filters (BDF's) performance rapidly deteriorated. This was mainly attributed to fine grinding i.e., about 85% < 25 microns. The phosphate cake produced by BDF was sloppy and posed problems in handling and transportation. The sloppier the product the more inefficient in loading and transportat-ion'. Thus the most daunting task was to reduce moisture content of phosphate cake from about 22% to 13-15%. This paper discusses the most critical role played by nano-technology in tackling this problem

Richard Eberhart’s Poetic Theory: Art and Craft

This paper is a maiden attempt to bring a promising, independent and prolific poet, richard eberhart to the fore, and to focus attention on the most dominating and pervasive theme in his poetry. His central theme of mortality is like a lofty mountain that dominates the entire landscape of his works. No matter what the road the reader takes, what pass he treads, he would find the mountain bursting on his vision at every turn of the way and at every parting of the hills. The secret of his upheld popularity rests on his uniquely strong individuality, romantic mould, spasmodic vigor, simplicity of expression and a deep concern for mankind. Kenneth Rexroth has rightly remarked that Eberhart is the poet of the academies. His long teaching experience, in school, navy and colleges; ‘independent intelligence’ and imaginative fervor, confirm the indisputable statement. He is a poet who is greatly indebted to tradition as far as the influences are concerned but he owes equally to ‘traditionless’ experiments. He attempts neither influences nor ‘traditionless’ experiments for its own sake, unless it contributes to the aesthetic integrity. He is totally devoted and sincerely dedicated to the writing of poetry but never considers it as an accident. He has a high notion of poetry like the Emersonian transcendental value of poetry. He feels that a successful poem is a proportionate blending of feeling and ideas: Poetry is the heart and head. If it is all heart, it may become soft. If it is all head, it becomes arid. (Opp,5) Here is a poet who vows to live for poetry: Some of our best poets have died for poetry by suicide. Poets should not die but should live for it. I deplore the suicides of these people. (Ralph J.Mills. Richard Eberhart, 13