A Functorial Construction of Quantum Subtheories

We apply the geometric quantization procedure via symplectic groupoids proposed by E. Hawkins to the setting of epistemically restricted toy theories formalized by Spekkens. In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, we obtain a functor from the Frobenius algebra in \textbf{Rel} of the toy theories to the Frobenius algebra of stabilizer quantum mechanics.Comment: 19 page

Geometric Quantization and Epistemically Restricted Theories: The Continuous Case

It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called epistemic restrictions. Such restrictions have been recently formulated in terms of the symplectic geometry of the corresponding classical theory [19]. The purpose of this note is to describe, using this symplectic framework, how to obtain a C*-algebraic formulation for the epistemically restricted theories. In the case of continuous variables, following the groupoid quantization recipe of E. Hawkins, we obtain a twisted group C*-algebra which is the usual Moyal quantization of a Poisson vector space [12].Comment: In Proceedings QPL 2016, arXiv:1701.00242. 10 page

A complete graphical calculus for Spekkens' toy bit theory

While quantum theory cannot be described by a local hidden variable model, it is nevertheless possible to construct such models that exhibit features commonly associated with quantum mechanics. These models are also used to explore the question of {\psi}-ontic versus {\psi}-epistemic theories for quantum mechanics. Spekkens' toy theory is one such model. It arises from classical probabilistic mechanics via a limit on the knowledge an observer may have about the state of a system. The toy theory for the simplest possible underlying system closely resembles stabilizer quantum mechanics, a fragment of quantum theory which is efficiently classically simulable but also non-local. Further analysis of the similarities and differences between those two theories can thus yield new insights into what distinguishes quantum theory from classical theories, and {\psi}-ontic from {\psi}-epistemic theories. In this paper, we develop a graphical language for Spekkens' toy theory. Graphical languages offer intuitive and rigorous formalisms for the analysis of quantum mechanics and similar theories. To compare quantum mechanics and a toy model, it is useful to have similar formalisms for both. We show that our language fully describes Spekkens' toy theory and in particular, that it is complete: meaning any equality that can be derived using other formalisms can also be derived entirely graphically. Our language is inspired by a similar graphical language for quantum mechanics called the ZX-calculus. Thus Spekkens' toy bit theory and stabilizer quantum mechanics can be analysed and compared using analogous graphical formalisms.Comment: Major revisions for v2. 22+7 page

Cohomology of Toroidal Orbifold Quotients

Let $\phi:\Z/p\to GL_{n}(\Z)$ denote an integral representation of the cyclic group of prime order $p$. This induces a $\Z/p$-action on the torus $X=\R^{n}/\Z^{n}$. The goal of this paper is to explicitly compute the cohomology groups $H^{*}(X/\Z/p;\Z)$ for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group $\Gamma =\Z^n\rtimes\Z/p$ with prime holonomy.Comment: Final version. Accepted for publication in the Journal of Algebr

Frequencies of Near Regular Structures Using the Results of the Corresponding Regular Structures

In this paper a method is presented for calculating the eigenvalues of perturbed matrices corresponding to their initial and unperturbed state. In other word, instead of solving the eigenvalue problem of perturbed matrix with size (n x n), only it is sufficient to solve eigenvalue problem for a matrix with dimension (m x m) where m is less than n and their difference (n – m) is considerable. By means of this method, eigenvalues and frequencies of near regular structures considering those of the corresponding regular structures are calculated

Computing the Szeged Index of Two Type Dendrimer Nanostars

In this paper we compute the szeged index of the first and second type of dendrimer nanostar

Subarachnoid hemorrhage:unusual situations leading to sah and underlying principles of physics behind its complications

Multiple authors have identified the most unusual novel associations as precipitant factors of subarachnoid hemorrhage and the knowledge of these and pathogenesis in background is necessary to suspect and therefore timely diagnose subarachnoid bleed and understand the mechanism of its subsequent complications. Objective: We herein describe unusual causes of subarachnoid bleed reported in various case reports with a comprehensive but elaborative review describing underlying pathogenesis and physiological mechanisms behind these precipitants and complications. Evidence Review: We sorted unusual causes of subarachnoid hemorrhage from literature review. By conducting meticulous scrutinization on search engines likePubmed®, Medline ®, Medline Plus ®, PubMed Central ®, MedNets®, Medbioworld®, Journal Watch® and Pakmedinet®; we found many novel associations using the key words: “Hemorrhagic stroke; subarachnoid hemorrhage; unusual precipitants; novel causes; pathogenesis; physical principles; aneurysms”. Findings: Novel associations of subarachnoid bleed include coagulopathies, lumbar puncture, degenerative vascular diseases, herpes encephalitis, sexual intercourse, bee sting, Conn’s syndrome and likewise many others. The basis of pathogenesis and its complications lies in understanding the complexity of relationship between the dynamics of intracranial pressure, volume and flow. Conclusions and Relevance: Understanding the physiology of exchange of force between different intracranial contents is the key to learn the mechanics of complicated brain injuries in SAH. Identifying the most unusual novel associations as precipitant factors of subarachnoid hemorrhage and the knowledge of these and the pathogenesis behind complications is necessary to suspect and therefore timely diagnose subarachnoid bleed.It may also help generate newer ideas for management in SAH

Punch problem for initially stressed neo hookean solids

The paper reports the indentation of a semi-infinite, initially stressed elastic medium under the action of an axisymmetric rigid punch pressing the medium normally. Th~ problem has been considered within the framework of incremental deformation theory for neo-Hookean solids. Using the Hankel's transformation, the distributions of incremental stress and strain have been obtained. Indentations by a flat-ended c and a conical punch have been obtained as special cases and these effects have been studied numerically and presented in the form of curves. This problem has defence application as many launching pads and firing machines have some neo-Hookean solids as buffer which bear enormous impact or punch during the action of the machine