1,597 research outputs found
Algebraic Dependencies and PSPACE Algorithms in Approximative Complexity
No full textTesting whether a set f of polynomials has an algebraic dependence is a basic problem with several applications. The polynomials are given as algebraic circuits. Algebraic independence testing question is wide open over finite fields (Dvir, Gabizon, Wigderson, FOCS'07). Previously, the best complexity known was NP^{#P} (Mittmann, Saxena, Scheiblechner, Trans.AMS'14). In this work we put the problem in AM cap coAM. In particular, dependence testing is unlikely to be NP-hard and joins the league of problems of "intermediate" complexity, eg. graph isomorphism & integer factoring. Our proof method is algebro-geometric- estimating the size of the image/preimage of the polynomial map f over the finite field. A gap in this size is utilized in the AM protocols.
Next, we study the open question of testing whether every annihilator of f has zero constant term (Kayal, CCC'09). We give a geometric characterization using Zariski closure of the image of f; introducing a new problem called approximate polynomials satisfiability (APS). We show that APS is NP-hard and, using projective algebraic-geometry ideas, we put APS in PSPACE (prior best was EXPSPACE via Gröbner basis computation). As an unexpected application of this to approximative complexity theory we get- over any field, hitting-sets for overline{VP} can be verified in PSPACE. This solves an open problem posed in (Mulmuley, FOCS'12, J.AMS 2017); greatly mitigating the GCT Chasm (exponentially in terms of space complexity)
Algebraic Independence over Positive Characteristic: New Criterion and Applications to Locally Low Algebraic Rank Circuits
No full textThe motivation for this work comes from two problems--test algebraic independence of arithmetic circuits over a field of small characteristic, and generalize the structural property of algebraic dependence used by (Kumar, Saraf CCC'16) to arbitrary fields.
It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-time algorithm to test algebraic independence. Over small characteristic, the Jacobian criterion fails and there is no subexponential time algorithm known. This problem could well be conjectured to be in RP, but the current best algorithm puts it in NP^#P (Mittmann, Saxena, Scheiblechner Trans.AMS'14). Currently, even the case of two bivariate circuits over F_2 is open. We come up with a natural generalization of Jacobian criterion, that works over all characteristic. The new criterion is efficient if the underlying inseparable degree is promised to be a constant. This is a modest step towards the open question of fast independence testing, over finite fields, posed in (Dvir, Gabizon, Wigderson FOCS'07).
In a set of linearly dependent polynomials, any polynomial can be written as a linear combination of the polynomials forming a basis. The analogous property for algebraic dependence is false, but a property approximately in that spirit is named as ``functional dependence'' in (Kumar, Saraf CCC'16) and proved for zero or large characteristic. We show that functional dependence holds for arbitrary fields, thereby answering the open questions in (Kumar, Saraf CCC'16). Following them we use the functional dependence lemma to prove the first exponential lower bound for locally low algebraic rank circuits for arbitrary fields (a model that strongly generalizes homogeneous depth-4 circuits). We also recover their quasipoly-time hitting-set for such models, for fields of characteristic smaller than the ones known before.
Our results show that approximate functional dependence is indeed a more fundamental concept than the Jacobian as it is field independent. We achieve the former by first picking a ``good'' transcendence basis, then translating the circuits by new variables, and finally approximating them by truncating higher degree monomials. We give a tight analysis of the ``degree'' of approximation needed in the criterion. To get the locally low algebraic rank circuit applications we follow the known shifted partial derivative based methods
Reading: Amit Majmudar
No full textBecause of COVID-19 this event is canceled.
Amit Majmudar, a multi-genre author and translator, offers a Sacred Arts Festival reading that explores the concept of Building Bridges.
Co-sponsored by the Department of English and the Sacred Arts Festival
sj-docx-1-pie-10.1177_09544089221112071 - Supplemental material for Empirical modeling and optimization of kerf characteristics in Nd-YAG laser cutting of Al 6061-T6 sheet
No full textSupplemental material, sj-docx-1-pie-10.1177_09544089221112071 for Empirical modeling and optimization of kerf characteristics in Nd-YAG laser cutting of Al 6061-T6 sheet by Amit Sharma, Priyanka Joshi and Kuldeep K Saxena in Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering</p
Exploring young students creativity: The effect of model eliciting activities
No full textThe aim of this paper is to show how engaging students in real-life mathematical situations can stimulate their mathematical creative thinking. We analyzed the mathematical modeling of two girls, aged 10 and 13 years, as they worked on an authentic task involving the selection of a track team. The girls displayed several modeling cycles that revealed their thinking processes, as well as cognitive and affective features that may serve as the foundation for a methodology that uses model-eliciting activities to promote the mathematical creative process
Ageing and temperature-dependent behaviour of CdS nanoparticles
No full textNanoparticles of inorganinc semiconductors in the form of coloids have attracted researchers due to their interesting optical properties. We report the process of the controlled coalescence of the nanoparticles in a colloid with time and also with temperature. Cadmium sulfide (CdS) nanoparticles were prepared in ethylene glycol (EG). The size of the particles was estimated by X-ray diffraction and transmission electron microscopy and matched with the optical absorption data. The particles in the EG matrix were subjected to controlled annealing and the shift in the absorption edge towards its bulk value (similar to 2.4 eV) was monitored. The change in the band gap value has been used to calculate the increasing particle radii using the effective-mass model. A similar effect is also reported with ageing of these particulates. (C) 2009 WILEY-VCH Verlag GmBH & co. KGaA, Weinhei
Quad-band circularly polarized super-wideband MIMO antenna for wireless applications
No full textIn this article, a Super-wideband (2.6–22 GHz) two-elements multiple-input-multiple-output antenna (MIMO) is presented with a dimension of 49 × 54.5 × 1.6 mm3 on an FR-4 substrate. The antenna is also exhibited dual circular polarization (RHCP and LHCP) simultaneously at two separate ports at four frequencies of 5.2, 11.5, 14.66, and 16.75 GHz, which are extensively utilized for WLAN, X, and Ku-band applications. Four EBG cells of various sizes have been installed across the feed line to maintain the antenna's efficiency and control the specific absorption rate (SAR). The antenna has a minimum isolation of 17 dB (20 dB for the important portion) in Super-wideband (SWB) and excellent diversity performance. Simulated results of antenna-like return loss, isolation, and diversity parameters have also been verified experimentally, which are in the acceptable range. Also, the calculated maximum SAR at 10 g is 1.095 W/kg with the head voxel model at 3.5 GHz
Reviewing the Author-Function in the Age of Wikipedia
No full textIn Reviewing the Author-Function in the Age of Wikipedia, Amit Ray and Erhardt Graeff examine how wiki technology challenges traditional concepts of authorship and authority in knowledge production. The authors build on poststructuralist theory, particularly Roland Barthes\u27s Death of the Author and Michel Foucault\u27s concept of the author-function, to analyze how wikis destabilize individual authorship in favor of collaborative, community-driven content creation.
The essay argues that wikis represent a fundamental shift from the Romantic notion of the solitary author-genius to what they term the wiki writing process —a dynamic system where traditional roles of reader, writer, and editor blur into a unified community of users. Using Wikipedia as a primary case study, the authors demonstrate how the platform\u27s structure (article, discussion, and history pages) creates a digital palimpsest that archives all contributions while enabling continuous revision.
Through analysis of Wikipedia\u27s editing patterns and community oversight mechanisms, Ray and Graeff show how wikis embody poststructuralist principles in practice, creating what they call serial collaborations that exist in perpetual flux. The authors conclude that wikis represent an evolved form of textual production that realizes Foucault\u27s vision of discourse freed from traditional authorial constraints, offering new possibilities for collaborative knowledge creation while challenging established notions of intellectual authority and ownership
The Architecture of India
No full textBook review of "India: Modern Architecture in History" and author interview with Peter Scriver and Amit Srivastav
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