Miracle-dz/UniFAR-FTUs huggingface dataset:
Topological Quantum Information, Khovanov Homology and the Jones Polynomial

In this paper we give a quantum statistical interpretation for the bracket polynomial state sum and for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones polynomial. This algorithm is useful for its conceptual simplicity, and it applies to all values of the polynomial variable that lie on the unit circle in the complex plane. Letting C(K) denote the Hilbert space for this model, there is a natural unitary transformation U from C(K) to itself such that = where |F> is a sum over basis states for C(K). The quantum algorithm arises directly from this formula via the Hadamard Test. We then show that the framework for our quantum model for the bracket polynomial is a natural setting for Khovanov homology. The Hilbert space C(K) of our model has basis in one-to-one correspondence with the enhanced states of the bracket state summmation and is isomorphic with the chain complex for Khovanov homology with coefficients in the complex numbers. We show that for the Khovanov boundary operator d defined on C(K) we have the relationship dU + Ud = 0. Consequently, the unitary operator U acts on the Khovanov homology, and we therefore obtain a direct relationship between Khovanov homology and this quantum algorithm for the Jones polynomial. The formula for the Jones polynomial as a graded Euler characteristic is now expressed in terms of the eigenvalues of U and the Euler characteristics of the eigenspaces of U in the homology. The quantum algorithm given here is inefficient, and so it remains an open problem to determine better quantum algorithms that involve both the Jones polynomial and the Khovanov homology.
Dynamical invariants for variable quadratic Hamiltonians

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schrödinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
Investigation of quantum fluctuations in a nonlinear interferometer with harmonic generation and coherent interaction of light and CS atoms

Srinivasan, Prashant Ph.D., Purdue University, December 2012. Investigation of quantum fluctuations in a nonlinear interferometer with harmonic generation and coherent interaction of light and Cs atoms . Major Professor: Zhe-Yu Jeff Ou. In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-toNoise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimental arrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements. PART I: QUANTUM FLUCTUATIONS IN A NONLINEAR INTERFEROMETER WITH HARMONIC GENERATION
Non-linear Recurrences that Quite Unexpectedly Generate Rational Numbers

Non-linear recurrences which generate integers in a surprising way have been studied by many people. Typically people study recurrences that are linear in the highest order term. In this paper I consider what happens when the recurrence is not linear in the highest order term. In this case we no longer produce a unique sequence, but we sometimes have surprising results. If the highest order term is raised to the $m^{th}$ power we expect answers to have $m^{th}$ roots, but for some specific recurrences it happens that we generate rational numbers ad infinitum. I will give a general example in the case of a first order recurrence with $m=2$, and a more specific example that is order 3 with $m=2$ which comes from a generalized Somos recurrence.
Pseudo-Hermitian Representation of Quantum Mechanics

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools, present their utility in establishing a lucid and precise formulation of a unitary quantum theory based on a non-Hermitian Hamiltonian, and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as ${\mathcal{P}\mathcal{T}}$, the true meaning and significance of the so-called charge operators $\mathcal{C}$ and the ${\mathcal{C}\mathcal{P}\mathcal{T}}$-inner products,.
Stock Market Prediction Using Machine Learning Techniques

Predicting the future in all the areas using machine learning techniques was the recent research in the current scenario. Stock market is one among them which needs the prediction future market to invest in the new enterprise or to sell their existing shares to get profit. This need the efficient prediction technique which studies the previous exchanges of stock market and gives the future prediction based on that. This article proposed the prediction system of stock market price based on the exchange takes place in previous scenario. The system studies the diversing effect of market price of product in a particular time gap and analyze its future trend whether it’s loss or gain. During the system of thinking about diverse strategies and variables that should be taken into account, we observed out that strategies like random forest, Support vector machine and regression algorithm. Support vector regression is a beneficial and effective gadget gaining knowledge of approach to apprehend sample of time collection dataset. The data collected for the four years duration which was accumulated to get the expecting prices of the share of the firm. It can produce true prediction end result if the fee of essential parameters may be decided properly. It has been located that the guide vector regression version with RBF kernel indicates higher overall performance while in comparison with different models.
Superintegrability of the Caged Anisotropic Oscillator

We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but additionally with barrier terms describing repulsive forces from the principal planes. This confines the classical motion to a sector bounded by the principal planes, or cage. In 3 degrees, there are five isolating integrals of motion, ensuring that all bound trajectories are closed and strictly periodic. Three of the integrals are quadratic in the momenta, the remaining two are polynomials of order 2(l+m-1) and 2(l+n-1). In the quantum problem, the eigenstates are multiply degenerate, exhibiting multiple copies of the fundamental pattern of the symmetry group SU(3).
Transforming Growth Factor ÃŸlSuppresses Genomic Instability Independent of a G! Arrest, p53, and Rb

Alterations in expression of or responsiveness to transforming growth factor Â¡'i(TGF-ÃŸ)are frequently found in human and animal epithelial cancers and are thought to be important for loss of growth control in the neoplastic cell. We show here that keratinocyte cell lines from mice with a targeted deletion of the TGF-ÃŸl gene have significantly increased fre quencies of gene amplification in response to the drug /V-phosphonoacetyl- i -asparÃ an- (PALA) compared to TGF-ÃŸl-expressing control keratinocyte cell lines. In contrast to the control lines, the PALA-mediated G, arrest did not occur in the TGF-ÃŸl null keratinocytes despite the presence of wild-type p53 in both genotypes. Exogenous TGF-ÃŸl suppresses gene amplification in the null keratinocytes at concentrations that do not cause a G, growth arrest and in human tumor cell lines that are insensitive to TGF-ÃŸl-mediated growth inhibition. The pathway of TGF-ÃŸl suppres sion is independent of Oiep53 and Kb genes, but requires an intact TGF-ÃŸ type 11receptor. These studies reveal a novel TGF-ÃŸ-mediated pathway regulating genomic stability and suggest that defects in TGF-ÃŸsignaling may have profound effects on tumor progression independent of cell proliferation.
RCC1 and ERCC1 variants modify malignant mesothelioma risk: case–control study

Malignant pleural mesothelioma (MPM) is a rare aggressive tumor associated with asbestos exposure. The possible role of genetic factors has also been suggested and MPM has been associated with single nucleotide polymorphisms (SNPs) of xenobiotic and oxidative metabolism enzymes. We have identified an association of the DNA repair gene XRCC1 with MPM in the population of Casale Monferrato, a town exposed to high asbestos pollution. To extend this observation we examined 35 SNPs in 15 genes that could be involved in MPM carcinogenicity in 220 MPM patients and 296 controls from two case–control studies conducted in Casale (151 patients, 252 controls) and Turin (69 patients, 44 controls), respectively. Unconditional multivariate logistic regression was used to estimate odds ratios (ORs) and 95% confidence intervals (95% CIs). Two DNA repair genes were associated with MPM, i.e. XRCC1 and ERCC1. Considering asbestos-exposed only, the risk increased with the increasing number of XRCC1399Q alleles (Casale: OR = 1.44, 95%CI 1.02–2.03; Casale + Turin: OR = 1.34, 95%CI 0.98–1.84) or XRCC1 −77T alleles (Casale + Turin: OR = 1.33, 95%CI 0.97–1.81). The XRCC1-TGGGGGAACAGA haplotype was significantly associated with MPM (Casale: OR = 1.76, 95%CI 1.04–2.96). Patients heterozygotes for ERCC1 N118N showed an increased OR in all subjects (OR = 1.66, 95%CI 1.06–2.60) and in asbestos-exposed only (OR = 1.59, 95%CI 1.01–2.50). When the dominant model was considered (i.e. ERCC1 heterozygotes CT plus homozygotes CC versus homozygotes TT) the risk was statistically significant both in all subjects (OR = 1.61, 95%CI 1.06–2.47) and in asbestos-exposed only (OR = 1.56, 95%CI 1.02–2.40). The combination of ERCC1 N118N and XRCC1 R399Q was statistically significant (Casale: OR = 2.02, 95%CI 1.01–4.05; 95%C sed s Casale + Turin: OR = 2.39, hypothesis that an increa
Canonical bases and quantum coordinate ring

Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized enveloping algebra. It is shown that the quotient algebras inherit canonical bases from the modified quantized enveloping algebra and are dual to the quantum coordinate ring defined by Kashiwara for symmetrizable Kac-Moody algebra $\mathfrak g$.
Constraining the body mass range of Anzu wyliei (Theropoda: Caenagnathidae) using volumetric and extant–scaling methods

Vertebrate Anatomy Morphology Palaeontology is an open access journal http://ejournals.library. ualberta.ca/index.php/VAMP Article copyright by the author(s). This open access work is distributed under a Creative Commons Attribution 4.0 International (CC By 4.0) License, meaning you must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. INTRODUCTION
On monomorphic topological functors with finite supports

We prove that a monomorphic functor $F:Comp\to Comp$ with finite supports is epimorphic, continuous, and its maximal $\emptyset$-modification $F^\circ$ preserves intersections. This implies that a monomorphic functor $F:Comp\to Comp$ of finite degree $deg F\le n$ preserves (finite-dimensional) compact ANR's if the spaces $F\emptyset$, $F^\circ\emptyset$, and $Fn$ are finite-dimensional ANR's. This improves a known result of Basmanov.
Effect of Cold Diet and Diet at Room Temperature on Post-Tonsillectomy Pain in Children

Introduction: The present study aimed to compare the effect of cold diet and diet at room temperature on post-tonsillectomy pain in children. Materials and Methods: In the present study a total of 120 children within the age range of 4-12 years who underwent tonsillectomy were randomly assigned to two groups, namely group C with a cold-served diet and group room temperaturewith a room-temperature-served diet postoperatively. Each patient’s post-operative pain was evaluated using the Face, Legs, Activity, Cry, Consolability (FLACC) scale prior to oral diet initiation after the operation, before thesecond acetaminophen dose, before the next day breakfast, and before discharge. Results: Out of 103 children, 48 and 55 children were femaleand male, respectively. The average age of the children was 7 years and 2 months. There was no significant difference in gender and age between the two groups. There were no significant differences in the mean scores of FLACC scale between the two groups at different times, including before starting an oral diet (P>0.15), before the second dose of acetaminophen (P>0.22), before the next day breakfast (P>0.32), and before discharge (P>0.83). In terms of bleedingfrequency, as well as nausea and vomiting, no significant difference was observed between the two groups. Conclusion: The obtained results of this study indicated that using cold liquids and foods after tonsillectomy did not have a significant effect on post-tonsillectomy pain in children. According to the findings, it is not rational to advise the mother or the child about the temperature of fluids and foods consumed post-tonsillectomy.
Snow event classi(cid:28)cation with a 2D video disdrometer - a decision tree approach

Snowfall classi(cid:28)cation according to crystal type or degree of riming of the snow(cid:29)akes is import for many atmospheric processes, e.g. wet deposition of aerosol particles. 2D video disdrometers (2DVD) have recently proved their capability to measure micro physical parameters of snowfall. The present work has the aim of classifying snowfall according to micro physical properties of single hydrometeors (e.g. shape and fall velocity) measured by means of a 2DVD. The constraints for the shape and velocity parameters which are used in a decision tree for classi(cid:28)cation of the 2DVD measurements, are derived from detailed on-site observations, combining automatic 2DVD classi(cid:28)cation with visual inspection. The developed decision tree algorithm subdivides the detected events into three classes of dominating crystal type (single crystals, complex crystals and pellets) and three classes of dominating degree of riming (weak, moderate and strong). The classi(cid:28)cation results for the crystal type were validated with an independent data set proving the unambiguousness of the classi(cid:28)cation. In addition, for three long-term events, good agreement of the classi(cid:28)cation results with independently measured maximum dimension of snow(cid:29)akes, snow(cid:29)ake bulk density and surrounding temperature was found. The developed classi(cid:28)cation algorithm is applicable for wind speeds below 5 . 0 ms − 1 and has the advantage of being easily implemented by other users.
The nonlinear Poisson equation via a Newton-embedding procedure

This article considers the semilinear boundary value problem given by the Poisson equation, −Δu = f(u) in a bounded domain Ω ⊂ ℝ n (n > 2) with a smooth boundary. For the zero boundary value case, we approximate a solution using the Newton-embedding procedure. With the assumptions that f, f′, and f″ are bounded functions on ℝ, with f′ < 0, and Ω ⊂ ℝ3, the Newton-embedding procedure yields a continuous solution. This study is in response to an independent work which applies the same procedure, but assuming that f′ maps the Sobolev space H 1(Ω) to the space of Hölder continuous functions , and f(u), f′(u), and f″(u) have uniform bounds. In the first part of this article, we prove that these assumptions force f to be a constant function. In the remainder of the article, we prove the existence, uniqueness, and H 2-regularity in the linear elliptic problem given by each iteration of Newton's method. We then use the regularity estimate to achieve convergence.
Hybrid Wind/PV System Fed Induction Motor Drive Application

Nowadays, world insists conservation of energy due to the impletion of the non-renewable energy sources such as black coal, crude oil, and gas from earth. In India, power devastation plays a vital role since the decrease of the coal in the power plant. This paper provides an invasive solution by using renewable energy such as wind and solar to the power demand. In this paper both are combined to get the desired amount of energy. This design permits the two sources to supply the heap independently or at the same time contingent upon the power request. The innate way of this Cuk-SEPIC intertwined converter, extra info channels are not important to sift through high recurrence music. Consonant substance is inconvenient for the generator life expectancy, warming issues, and proficiency. The combined multi input rectifier arrange additionally permits Maximum Power Point Tracking (MPPT) to be utilized to concentrate most extreme power from the wind and sun when it is accessible. A versatile MPPT calculation will be utilized for the wind framework and a standard bother and watch technique will be utilized for the PV framework. Consequently, expansive voltage spikes over the principle switches are lifted and the effectiveness is moved forward. Here the low voltage push supports the selection of low voltage-evaluated MOSFETs for the decrease of both conduction misfortunes and cost. This demonstrates the proposed framework is likewise financially savvy and proficient. For the case here the framework is considered with the engine stack.
Customer RPE: Using customer performance to filter noise out of CEO incentive contracts

The “informativeness criterion” (Holmstrom 1982) states that any information item that is informative about a CEO’s effort be used in incentive contracting. Prior research documents negative incentive weights on industry peer performance in CEO contracting in what is known as “relative performance evaluation” (RPE). RPE improves the efficiency of incentive contracting by filtering noise from CEO performance measurement. We test whether the performance of a firm’s customer base is also used to improve incentive contracting, what we term “customer relative performance evaluation” (customer RPE). Consistent with customer RPE, we document a negative incentive weight on customer performance in CEO incentive contracts incremental to the negative incentive weight on performance of industry peers documented in prior research. Further, the negative incentive weight on customer performance is larger in absolute value for firms whose performance is more highly correlated with their customers’ performance, when the firm’s products/services are more specialized, and when the firm has lower operating flexibility. Moreover, the weight on customer performance decreases when the adverse incentives triggered by customer RPE are more costly.
TiO 2 -Supported Binary Metal Oxide Catalysts for Low-temperature Selective Catalytic Reduction of NO x with NH 3

: B inary metal oxide (MnO x -A/TiO 2 ) catalysts were prepared by adding the second metal to manganese oxides supported on titanium dioxide (TiO 2 ) , where A indicates Fe 2 O 3 , WO 3 , MoO 3 and Cr 2 O 3 . Their catalytic activity, N 2 selectivity and SO 2 poisonous tolerance were investigated. The catalytic performance at low temperature decreased in the following order: Mn-W/TiO 2 ＞ Mn-Fe/TiO 2 ＞ Mn-Cr/TiO 2 ＞ Mn-Mo/TiO 2 ， whereas the N 2 selectivity decreased in order: Mn-Fe/TiO 2 ＞ Mn-W/TiO 2 ＞ Mn-Mo/TiO 2 ＞ Mn-Cr/TiO 2 . In presence of 100ppm SO 2 and 6% H 2 O ， the NO x conversion of Mn-W/TiO 2 , Mn-Fe/TiO 2 , Mn-Mo/TiO 2 maintain 98.5%, 95.8% and 94.2% respectively after 8h at 120 ℃ at GHSV 12600h -1 . As effective promoters, WO 3 and Fe 2 O 3 can increase N 2 selectivity and the resistance to SO 2 of MnO x /TiO 2 significantly. The Fourier transform infrared spectrum (FTIR) spectra of NH 3 over WO 3 showed the presence of Lewis acid sites. The results suggest that WO 3 is the best promoter of MnO x /TiO 2 , Mn-W/TiO 2 is one of the most active catalysts for low temperature selective catalytic reduction of NO with NH 3
Almost commuting matrices, localized Wannier functions, and the quantum Hall effect

For models of noninteracting fermions moving within sites arranged on a surface in three-dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are K-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward and does not require translational invariance or introduce a flux torus. We further show that there is a Z2 index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as t.
Scalars, Monads, and Categories

This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads. These interrelations will be expressed in terms of "triangles of adjunctions", involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions.