Intersection multiplicities over Gorenstein rings

We construct a complex of free-modules over a Gorenstein ring R of dimension five, for which the Euler characteristic and Dutta multiplicity are different. This complex is the resolution of an R-module of finite length and finite projective dimension. As a consequence, the ring R has a nonzero Todd class tau_3(R) and a bounded free complex whose local Chern character does not vanish on this class. In the course of our work, we construct a module N of finite length and finite projective dimension over the hypersurface A=K[u,v,w,x,y,z]/(ux+vy+wz), such that the Serre intersection multiplicity of the modules N and A/(u,v,w)A is -2

Low Cost Swarm Based Diligent Cargo Transit System

The goal of this paper is to present the design and development of a low cost cargo transit system which can be adapted in developing countries like India where there is abundant and cheap human labour which makes the process of automation in any industry a challenge to innovators. The need of the hour is an automation system that can diligently transfer cargo from one place to another and minimize human intervention in the cargo transit industry. Therefore, a solution is being proposed which could effectively bring down human labour and the resources needed to implement them. The reduction in human labour and resources is achieved by the use of low cost components and very limited modification of the surroundings and the existing vehicles themselves. The operation of the cargo transit system has been verified and the relevant results are presented. An economical and robust cargo transit system is designed and implemented.Comment: 6 pages, 9 figures, 1 block diagra

A Generative Model For Zero Shot Learning Using Conditional Variational Autoencoders

Zero shot learning in Image Classification refers to the setting where images from some novel classes are absent in the training data but other information such as natural language descriptions or attribute vectors of the classes are available. This setting is important in the real world since one may not be able to obtain images of all the possible classes at training. While previous approaches have tried to model the relationship between the class attribute space and the image space via some kind of a transfer function in order to model the image space correspondingly to an unseen class, we take a different approach and try to generate the samples from the given attributes, using a conditional variational autoencoder, and use the generated samples for classification of the unseen classes. By extensive testing on four benchmark datasets, we show that our model outperforms the state of the art, particularly in the more realistic generalized setting, where the training classes can also appear at the test time along with the novel classes

Unparticle physics in diphoton production at the CERN LHC

We have considered the di-photon production with unparticle at LHC. The contributions of spin-0 and spin-2 unparticle to the di-photon production are studied in the invariant mass and other kinematical distributions, along with their dependencies on the model dependent parameters. The signal corresponding to the unparticle is significant for moderate coupling constant values.Comment: 17 pages, 15 eps figure

Morphometric analysis of sella turcica in North Indian population: a radiological study

Background:The purpose of this study was to describe the morphology and measure the size of the sella turcica in North Indian population.Methods:Lateral cephalometric radiographs of 180 individuals (90 males and 90 females) with an age range of 12 - 65 years were taken. Morphology of sella turcica was studied and various measurements were taken to determine the shape of the sella. Statistical analysis was done to calculate differences in dimensions and to establish if any, relationship exists between age, sex and the morphometry of sella turcica.Results:The study found that sella turcica presented with a normal morphology in only 28 per cent of the subjects. A significant difference in linear dimensions between genders was found in sella height and width. When age was evaluated, some dimensions showed negative correlation with the age. Sella size of the older age group was as a rule larger than the younger age.Conclusion: Pathological enlargement of the pituitary fossa can be detected by this technique and may also be helpful in providing data in the assessment of racial, gender, age specific variation in the skull

High-Voltage Micro-Ampere Current Regulator

A high-voltage micro-ampere current regulator which can provide stable current regulation to a corona discharge without requiring a portion of that corona discharge to be sampled. The current regulator can optionally include a first feed-back circuit which provides rapidly-adapting current regulation, and an optional second feedback circuit which provides slowly-adapting current regulation to avoid changes in corona discharge due to oxidation of the corona emitter

Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states

One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal states with a bond dimension growing polynomially with the system size. In the regime of sufficiently low temperatures, which is particularly important for practical applications, the existing techniques do not yield optimal bounds. Here, we propose a new thermal area law that holds for generic many-body systems on lattices. We improve the temperature dependence from the original $\mathcal{O}(\beta)$ to $\tilde{\mathcal{O}}(\beta^{2/3})$, thereby suggesting diffusive propagation of entanglement by imaginary time evolution. This qualitatively differs from the real-time evolution which usually induces linear growth of entanglement. We also prove analogous bounds for the R\'enyi entanglement of purification and the entanglement of formation. Our analysis is based on a polynomial approximation to the exponential function which provides a relationship between the imaginary-time evolution and random walks. Moreover, for one-dimensional (1D) systems with $n$ spins, we prove that the Gibbs state is well-approximated by a matrix product operator with a sublinear bond dimension of $e^{\sqrt{\tilde{\mathcal{O}}(\beta \log(n))}}$. This allows us to rigorously establish, for the first time, a quasi-linear time classical algorithm for constructing an MPS representation of 1D quantum Gibbs states at arbitrary temperatures of $\beta = o(\log(n))$. Our new technical ingredient is a block decomposition of the Gibbs state, that bears resemblance to the decomposition of real-time evolution given by Haah et al., FOCS'18.Comment: 20 pages + 29 pages, 9 figure