Quasi-polynomial Hitting-set for Set-depth-Delta Formulas

We call a depth-4 formula C set-depth-4 if there exists a (unknown) partition (X_1,...,X_d) of the variable indices [n] that the top product layer respects, i.e. C(x) = \sum_{i=1}^k \prod_{j=1}^{d} f_{i,j}(x_{X_j}), where f_{i,j} is a sparse polynomial in F[x_{X_j}]. Extending this definition to any depth - we call a depth-Delta formula C (consisting of alternating layers of Sigma and Pi gates, with a Sigma-gate on top) a set-depth-Delta formula if every Pi-layer in C respects a (unknown) partition on the variables; if Delta is even then the product gates of the bottom-most Pi-layer are allowed to compute arbitrary monomials. In this work, we give a hitting-set generator for set-depth-Delta formulas (over any field) with running time polynomial in exp(({Delta}^2 log s)^{Delta - 1}), where s is the size bound on the input set-depth-Delta formula. In other words, we give a quasi-polynomial time blackbox polynomial identity test for such constant-depth formulas. Previously, the very special case of Delta=3 (also known as set-multilinear depth-3 circuits) had no known sub-exponential time hitting-set generator. This was declared as an open problem by Shpilka & Yehudayoff (FnT-TCS 2010); the model being first studied by Nisan & Wigderson (FOCS 1995). Our work settles this question, not only for depth-3 but, up to depth epsilon.log s / loglog s, for a fixed constant epsilon < 1. The technique is to investigate depth-Delta formulas via depth-(Delta-1) formulas over a Hadamard algebra, after applying a `shift' on the variables. We propose a new algebraic conjecture about the low-support rank-concentration in the latter formulas, and manage to prove it in the case of set-depth-Delta formulas.Comment: 22 page

Jacobian hits circuits: Hitting-sets, lower bounds for depth-D occur-k formulas & depth-3 transcendence degree-k circuits

We present a single, common tool to strictly subsume all known cases of polynomial time blackbox polynomial identity testing (PIT) that have been hitherto solved using diverse tools and techniques. In particular, we show that polynomial time hitting-set generators for identity testing of the two seemingly different and well studied models - depth-3 circuits with bounded top fanin, and constant-depth constant-read multilinear formulas - can be constructed using one common algebraic-geometry theme: Jacobian captures algebraic independence. By exploiting the Jacobian, we design the first efficient hitting-set generators for broad generalizations of the above-mentioned models, namely: (1) depth-3 (Sigma-Pi-Sigma) circuits with constant transcendence degree of the polynomials computed by the product gates (no bounded top fanin restriction), and (2) constant-depth constant-occur formulas (no multilinear restriction). Constant-occur of a variable, as we define it, is a much more general concept than constant-read. Also, earlier work on the latter model assumed that the formula is multilinear. Thus, our work goes further beyond the results obtained by Saxena & Seshadhri (STOC 2011), Saraf & Volkovich (STOC 2011), Anderson et al. (CCC 2011), Beecken et al. (ICALP 2011) and Grenet et al. (FSTTCS 2011), and brings them under one unifying technique. In addition, using the same Jacobian based approach, we prove exponential lower bounds for the immanant (which includes permanent and determinant) on the same depth-3 and depth-4 models for which we give efficient PIT algorithms. Our results reinforce the intimate connection between identity testing and lower bounds by exhibiting a concrete mathematical tool - the Jacobian - that is equally effective in solving both the problems on certain interesting and previously well-investigated (but not well understood) models of computation

Saving of Power in Wireless Power Transmission System using IR Sensor and Relay

As all we know that today’s live is not possible for a moment if we think without electricity after our basic needs that are air, water, food, cloth and shelter. Because without it we can not think about our mobility, But it has also many disadvantages because of the transmission of electricity through wire which cause many time sock due to which living thing may get injured or many time they get unexpected death. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Hence for establishing the transmission of electricity without hazards today’s world started working on the removal of the net of the wires over the world and this is possible only by transmitting electricity wirelessly. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; This principle was early given by a charming and mysterious inventor and engineer Nikola Tesla(1891-1898) by inventing Tesla coil. But in wireless electricity transmission, there is a lot of wastage of energy when power is transferred to the load. If there is no loads are available around the receiving antenna(coil), power will be wasted and this is a one of the major disadvantage of this principle. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; So by using IR Sensor we can save this power from being waste which will allow the antenna to transmit the power only when the objects are available to receive this transmitted power

Design and characterization of convective thermal cyclers for high-speed DNA analysis

An ideal polymerase chain reaction (PCR) system should be capable of rapidly amplifying a wide range of targets in both single and multiplex formats. Unfortunately, the timescales and complexities involved in many existing technologies impose significant limitations on achievable throughput. Buoyancy driven PCR is emerging as a simplified version of thermally driven bio-analysis systems. Here, we demonstrate a simplified convectively driven thermocycler capable of performing single and multiplex PCR for amplicons ranging from 191 bp to 1.3 kb within 10 to 50 minutes using 10 to 25 µL reaction volumes. By positioning two independent thermoelectric heating elements along the perimeter of a flow loop reactor constructed using ordinary plastic tubing, a buoyancy-driven flow is established that continuously circulates reagents through temperature zones associated with the PCR process. Unlike conventional benchtop thermocyclers, this arrangement allows reactions to be performed without the need for dynamic temperature control of inactive hardware components while maintaining comparable product yields and requiring no modifications to standard PCR protocols. We also provide a general correlation that can be applied to design reactor geometries satisfying virtually any combination of reagent volume and cycling time. In addition to offering an attractive combination of cost and performance, this system is readily adaptable for portable battery powered operation, making it feasible to perform PCRbased assays in a broader array of settings

Review on Rasayana therapy to improve immunity for better health

Ayurvedic medicine has many rejuvenating herbs, traditionally known as Rasayana, which improve health, immunity, vigor, vitality and longevity, as well as protect against stress and help in boosting immunity power. Rasayana Chikitsa (rejuvenation) is a inimitable branch of Ayurveda. The word “Rasayana” means the way for attaining excellent Rasadi Dhatus. In Ayurveda, one of the major methods of presentation of positive health has been described i.e. Rasayana. This resistance power of the body, which prevents the development of diseases, is called as Immunity or Vyadhikshamatva. The ultimate aim of Rasayan therapy is to correct dosha disturbances and improve Agni and Dhatu function which overall improves strength, immunity. Basically, the application of Rasayan therapy comes in the perspective of premature ageing (Jara) and death. Rasayanas are used as preventive, curative and health promotive purpose

Dental Age Assessment using Demirjian’s Eight Teeth Method and Willems Method in a Tertiary Hospital

Introduction: Age estimation is an important aspect in forensic anthropology, as it can aid in the identification of the deceased, and can be used in cases of immigration, child abuse and criminal prosecution in living individuals. Dental age estimation is considered reliable and accurate, since tooth development is least affected by environmental factors compared to somatic growth. Methods: In total, 150 pre-orthodontic treatment radiographs from healthy individuals were assessed. These individuals were aged between 8 to 19 years. Dental age for these individuals was calculated by two methods: Demirjian’s eight teeth method and Willems method. For Willems method, seven teeth on the left side of mandible (except the third molar) were staged according to Demirjian’s staging, and for Demirjian’s eight teeth method, all eight teeth were staged. Results: The mean chronological ages were 13.6961±1.94384 years in males and 13.9204±2.63541 years in females. The mean estimated ages by Demirjian’s eight teeth method were 12.1856±1.73478 years and 11.7906±2.32344 years in males and females respectively. Similarly, the mean estimated ages by Willems method were 12.8958±1.46838 years in males and 12.6926±2.27807 years in females. Conclusions: Willems method and Demirjian’s eight teeth method underestimated the chronological age in the given population. Both methods showed excellent correlation with chronological age indicating their applicability in dental age estimation, with development of population specific scores

Integer Factoring Using Small Algebraic Dependencies

Integer factoring is a curious number theory problem with wide applications in complexity and cryptography. The best known algorithm to factor a number n takes time, roughly, exp(2*log^{1/3}(n)*log^{2/3}(log(n))) (number field sieve, 1989). One basic idea used is to find two squares, possibly in a number field, that are congruent modulo n. Several variants of this idea have been utilized to get other factoring algorithms in the last century. In this work we intend to explore new ideas towards integer factoring. In particular, we adapt the AKS primality test (2004) ideas for integer factoring. In the motivating case of semiprimes n=pq, i.e. p<q are primes, we exploit the difference in the two Frobenius morphisms (one over F_p and the other over F_q) to factor n in special cases. Specifically, our algorithm is polynomial time (on number theoretic conjectures) if we know a small algebraic dependence between p,q. We discuss families of n where our algorithm is significantly faster than the algorithms based on known techniques

Incremental and Decremental Nonparametric Discriminant Analysis for Face Recognition

Nonparametric Discriminant Analysis (NDA) possesses inherent advantages over Linear Discriminant Analysis (LDA) such as capturing the boundary structure of samples and avoiding matrix inversion. In this paper, we present a novel method for constructing an updated Nonparametric Discriminant Analysis (NDA) model for face recognition. The proposed method is applicable to scenarios where bursts of data samples are added to the existing model in random chunks. Also, the samples which degrade the performance of the model need to be removed. For both of these problems, we propose incremental NDA (INDA) and decremental NDA (DNDA) respectively. Experimental results on four publicly available datasets viz. AR, PIE, ORL and Yale show the efficacy of the proposed method. Also, the proposed method requires less computation time in comparison to batch NDA which makes it suitable for real time applications