Miracle-dz/UniFAR-FTUs huggingface dataset:
Topics in classical and quantum phase transitions

Classical and quantum phase transitions for several models are considered. First, a network of parallel superconducting wires weakly coupled together by the proximity effect described by the Ginzburg-Landau theory is studied by mapping onto N -distinguishable two dimensional quantum-mechanics problem with a perpendicular imaginary magnetic field. Using a mean-field approximation, the critical temperature for onset of interwire phase coherence is obtained for a given coupling. Second, the thermodynamic properties of a collection of N small Josephson junctions coupled to a single-mode resonant electromagnetic cavity is considered employing these models: (a) the model which includes all the quantum-mechanical levels of the junction, (b) the Dicke model with only the two lowest energy levels per junction, and (c) a modified Dicke model which contains an additional XY-like coupling between the junctions. In all cases, within a mean-field approximation, for an N -independent junction-cavity coupling, there is a critical junction number N above which there is a continuous transition from incoherence to coherence with decreasing T with a non-Bose distribution for the cavity photon occupation numbers. The third problem investigated is a disorder driven quantum phase transition in a class of transition metal oxides described by a single orbital Hubbard model at half filling. This model contains the interplay of disorder and transitions between phases with differing conducting and
A K-Band-selected Photometric Redshift Catalog in the Hubble Deep Field South: Sampling the Rest-Frame V Band to z = 3

We present the first results from the Faint Infra-Red Extragalactic Survey of the Hubble Deep Field South (HDF-S). Using a combination of deep near-infrared (NIR) data obtained with the Infrared Spectrograph and Array Camera at the VLT and the WFPC2 Hubble Space Telescope data, we construct a K-band–selected sample which is 50% and 90% complete for Ks,AB ≤ 23.5 and Ks,AB ≤ 22.0, respectively, where the magnitudes are measured over a 2. ″0 diameter aperture. For z ≤ 3, our selection by the K-band flux chooses galaxies based on wavelengths redder than the rest-frame V band, and so selects them in a way that is less dependent on their current star formation rates than selection in the rest-frame UV. We developed a new photometric redshift technique that models the observed spectral energy distribution (SED) with a linear combination of empirical galaxy templates. We tested this technique using 150 spectroscopic redshifts in the Hubble Deep Field North (HDF-N) from the Cohen et al. sample (published in 2000) and found Δz/(1 + z) ≈ 0.07 for z < 6. We show that we can derive realistic error estimates in zphot by combining the systematic uncertainties derived from the HDF-N with errors in zphot, which depend on the observed flux errors. We estimate photometric redshifts for 136 galaxies in the HDF-S from the full seven-band, 0.3–2.2 μm SED. In finding the correct zphot, our deep NIR data is important for breaking the redshift degeneracy between templates of identical observed optical colors. The redshift histogram of galaxies in the HDF-S shows distinct structure with a sharp peak at z ≈ 0.5 and a broad enhancement at z ∼ 1–1.4. We find that 12% of our galaxies with Ks,vega < 21 lie at z ≥ 2. While this is higher than the fraction predicted in ΩM = 1 hierarchical models of galaxy formation, we find that published predictions using pure luminosity evolution models produce too many bright galaxies at redshifts greater than unity. Finally, we use our broad wavelength coverage to measure the rest-frame UBV luminosities, Lrest, for z ≤ 3. There is a paucity of galaxies brighter than L ≥ 1.4 × 1010 h-2 L⊙ at z ∼ 1.5–2, similar to what Dickinson found for the HDF-N (published in 2001). However, zphot is particularly uncertain in this regime, and spectroscopic confirmation is required. We also note that at z > 2 we find very luminous galaxies with L ≥ 5 × 1010 h-2 L⊙ (for ΩM = 0.3, ΩΛ = 0.7, and H0 = 100 h km s-1 Mpc-1). Local B-band luminosity functions predict 0.1 galaxies in the redshift range 2 ≤ z ≤ 3.5 and with L ≥ 5 × 1010 h-2 L⊙,B, but we find nine. The discrepancy can be explained if L increases by a factor of 2.4–3.2 with respect to locally determined values. Random errors in the photometric redshift can also play a role, and spectroscopic confirmation of the redshifts of these bright galaxies is required.
Quantum Algebras Associated to Irreducible Generalized Flag Manifolds

Author(s): Tucker-Simmons, Matthew Bruce | Advisor(s): Rieffel, Marc A; Reshetikhin, Nicolai | Abstract: The first part of this thesis deals with certain properties of the quantum symmetric and exterior algebras of Type 1 representations of Uq(g) defined by Berenstein and Zwicknagl. We define a notion of a commutative algebra object in a coboundary category, and we prove that the quantum symmetric algebra of a module is the universal commutative algebra generated by that module. That is, the functor assigning to a module its quantum symmetric algebra is left adjoint to a forgetful functor. We also prove a conjecture of Berenstein and Zwicknagl, stating that the quantum symmetric and exterior cubes exhibit the same amount of "collapsing" relative to their classical counterparts. We prove that those quantum exterior algebras that are flat deformations of their classical analogues are Frobenius algebras. We also develop a rigorous framework for discussing continuity and limits of the structures involved as the deformation parameter q varies along the positive real line.The second part deals with quantum analogues of Clifford algebras and their application to the noncommutative geometry of certain quantum homogeneous spaces. We introduce the quantum Clifford algebra through its spinor representation via creation and annihilation operators on one of the flat quantum exterior algebras discussed in the first part. The proof that the spinor representation is irreducible relies on the Frobenius property discussed previously. We use this quantum Clifford algebra to revisit Krahmer's construction of a Dolbeault-Dirac-type operator on a quantized irreducible flag manifold. This operator is of the form d + d*, and we relate d to the boundary operator for the Koszul complex of a certain quantum symmetric algebra, which shows that d2 =0. This is a first step toward a Parthasarathy-type formula for the spectrum of the square of the Dirac operator.
Just Saiyan: Tail-trimming Human Monkeypox Virus Assemblies Emphasizes Resolvable Regions in Inverted Terminal Repeats to Improve the Resolution of Reference and Production Genomes for Genomic Surveillance.

Our ability to track the spread of the human monkeypox virus (hMPXV) during the ongoing monkeypox (hMPX) outbreak of 2022 relies on the availability of high-quality reference genomes. However, the way the information content of these genomes is organized in genome databases leaves room for interpretation. A current limitation of hMPXV genomic analysis is that the variability occurring in the inverted terminal repeats (ITRs) cannot be effectively resolved. This is because of shortcomings of the leading short-read sequencing and reference-guided assembly and variant calling used in the ongoing global hMPXV outbreak surveillance effort. Here I propose ITR tail-trimming, a simple no-cost reframing of how we organize hMPXV reference genomes and future assemblies. This approach is based on long terminal repeat (LTR) tail-trimming, which is a common practice in HIV sequence analysis. The main point of repeat sequence trimming is to remove problematic sequences while paying attention to limitations of mapping and variant calling in remaining repeat-associated (but ideally no longer repetitive) sequence. ITR tail-trimming would neutralize ITRs as distracting features at the read- and assembly-levels, allowing the global community to focus our efforts to track variability across hMPXV genomes.
Pushing frontiers in Carrier-Envelope Phase stabilization of ultrashort laser pulses

In the last decade, the measurement and stabilization of the carrier-envelope phase has become a mature technology, which offers diverse applications in the fields of frequency metrology and attosecond physics. The most limiting aspects of this technology are the achievable residual phase jitter and the long-term stability. The present thesis is dedicated to improvements of the carrier-envelope phase stabilization in response to these aspects. In order to realize such improvements, the fundamental noise sources are identified, and suitable measures for their reduction are proposed. It is shown that both, the measurement of the carrier-envelope phase as well as its control are corrupted by different noise contributions. On the one hand, the detection process is influenced by technical noise sources, which arise especially in the used nonlinear interferometers. It is demonstrated how such limitations can be minimized by a suitable choice of the interferometer topology. On the other hand, the detection noise in the electrooptic conversion represents a fundamental limitation, since the optical shot noise as well as the noise induced by the light detector inevitably influence the measurement of the carrier-envelope phase. A reduction of these constraints is solely achieved for higher detected light fluences, which are quantified in the framework of numerical calculations. On the basis of a numerical optimization of the spectral broadening process in a micro-structured fiber, an enormous improvement of the signal-to-noise ratio by 20 dB is obtained experimentally, which significantly reduces the limitation of detection noise. So far, the best stabilization results have been achieved with a feed-forward approach, which is based on an acousto-optical frequency shifter. This technique, however, suffers from several constraints that are mainly caused by varying dynamics of the carrier-envelope phase in oscillator pulse trains. A novel double stabilization scheme solves this issue by combining the feed-forward stabilization with a classical feedback loop. This method enabled a reduction of the residual phase jitter to an unprecedented value of 20milliradians, which corresponds to temporal fluctuations of the carrier-wave with respect to the envelope of only 8 attoseconds. Beyond that, several further concepts are introduced that are capable of stabilizing the CEP without any feedback to the laser oscillator. One of these concepts, referred to as the acoustic frequency comb, represents a pulsed feed-forward stabilization, which is specifically designed for the use in combination with a subsequent amplification stage. First experimental results indicate that residual phase jitters of less than 100milliradian are within reach also for amplified laser systems.
Number Theoretic Methods in Cryptography: Complexity lower bounds

I Preliminaries. - 1 Introduction. - 2 Basic Notation and Definitions. - 3 Auxiliary Results. - II Approximation and Complexity of the Discrete Logarithm. - 4 Approximation of the Discrete Logarithm Modulo p.- 5 Approximation of the Discrete Logarithm Modulo p - 1. - 6 Approximation of the Discrete Logarithm by Boolean Functions. - 7 Approximation of the Discrete Logarithm by Real and Complex Polynomials. - III Complexity of Breaking the Diffie-Hellman Cryptosystem. - 8 Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Key. - 9 Boolean Complexity of the Diffie-Hellman Key. - IV Other Applications. - 10 Trade-off between the Boolean and Arithmetic Depths of Modulo p Functions. - 11 Special Polynomials and Boolean Functions. - 12 RSA and Blum-Blum-Shub Generators of Pseudo-Random Numbers. - V Concluding Remarks. - 13 Generalizations and Open Questions. - 14 Further Directions.
Generalized diffusion and asymptotics induced by Tsallis entropy

We formulate and solve the diffusion equation over a previously studied field $\mathcal{R}$, whose construction was motivated by the Tsallis entropy composition property. We compare this solution with the solutions of the diffusion and of the porous medium equations. We comment on the asymptotics of such solutions for large values of their spatial and temporal variables. We present conclusions for the generalised operations inspired by the Tsallis entropy composition and their relations to hyperbolicity.
An exchangeable Kendall's tau for clustered data

This article introduces the exchangeable Kendall's tau as a nonparametric intraclass association measure in a clustered data frame and studies the sampling properties of an estimator of this quantity. Its asymptotic distribution is derived under a multivariate exchangeable model. Two applications of the proposed statistic are considered. The first is an estimator of the intraclass correlation coefficient for data drawn from an elliptical distribution. The asymptotic properties of this estimator are investigated under an extended random effects ANOVA model. The second is a semiparametric intraclass independence test based on the exchangeable Kendall's tau whose performance is assessed using Pitman efficiencies and a Monte Carlo study. The Canadian Journal of Statistics 42: 384–403; 2014 © 2014 Statistical Society of Canada
Parallel Algorithms for Combinatorial Search Problems

This thesis is a theoretical study of parallel algorithms for combinatorial search problems. In this thesis we present parallel algorithms for backtrack search, branch-and-bound computation and game-tree search. Our model of parallel computation is a network of processors communicating via messages. Our primary interest in a parallel algorithm is its speed-up over the sequential ones. Our goal is to design parallel algorithms that achieve a speed-up proportional to the number of processors used. We first study backtrack search that enumerates all solutions to a combinatorial problem. We propose a simple randomized method for parallelizing sequential backtrack search algorithms for solving enumeration problems. We show that, uniformly on all instances, this method is likely to achieve a nearly best possible speed-up. We then study the branch-and-bound method for solving combinatorial optimization problems. We present a randomized method called Local Best-First Search for parallelizing sequential branch-and-bound algorithms. We show that, uniformly on all instances, the execution time of this method is unlikely to exceed a certain inherent lower bound by more than a constant factor. In the rest of this thesis we study the problem of evaluation of game trees in parallel. We present a class of parallel algorithms that parallelize the "left-to-right" algorithm for evaluating AND/OR trees and the $\alpha$-$\beta$ pruning algorithm for evaluating MIN/MAX trees. We prove that the algorithm achieves a linear speed-up over the left-to-right algorithm on uniform AND/OR trees when the number of processors used is close to the height of the input tree. We conjecture that the same conclusion holds for the speed-up of the algorithm over the $\alpha$-$\beta$ pruning algorithm.
The Width of a Solar Coronal Mass Ejection and the Source of the Driving Magnetic Explosion: A Test of the Standard Scenario for CME Production

We show that the strength (BFlare) of the magnetic field in the area covered by the flare arcade following a CME-producing ejective solar eruption can be estimated from the final angular width (Final θCME) of the CME in the outer corona and the final angular width (θFlare) of the flare arcade: BFlare ≈ 1.4 [(Final θCME)/θFlare]2 G. We assume (1) the flux-rope plasmoid ejected from the flare site becomes the interior of the CME plasmoid; (2) in the outer corona (R > 2 R☉) the CME is roughly a "spherical plasmoid with legs" shaped like a lightbulb; and (3) beyond some height in or below the outer corona the CME plasmoid is in lateral pressure balance with the surrounding magnetic field. The strength of the nearly radial magnetic field in the outer corona is estimated from the radial component of the interplanetary magnetic field measured by Ulysses. We apply this model to three well-observed CMEs that exploded from flare regions of extremely different size and magnetic setting. One of these CMEs was an over-and-out CME, that is, in the outer corona the CME was laterally far offset from the flare-marked source of the driving magnetic explosion. In each event, the estimated source-region field strength is appropriate for the magnetic setting of the flare. This agreement (1) indicates that CMEs are propelled by the magnetic field of the CME plasmoid pushing against the surrounding magnetic field; (2) supports the magnetic-arch-blowout scenario for over-and-out CMEs; and (3) shows that a CME's final angular width in the outer corona can be estimated from the amount of magnetic flux covered by the source-region flare arcade.
Chemical reactions in the presence of surface modulation and stirring

We study the dynamics of simple reactions where the chemical species are confined on a general, time-modulated surface, and subjected to externally-imposed stirring. The study of these inhomogeneous effects requires a model based on a reaction-advection-diffusion equation, which we derive. We use homogenization methods to show that up to second order in a small scaling parameter, the modulation effects on the concentration field are asymptotically equivalent for systems with or without stirring. This justifies our consideration of the simpler reaction-diffusion model, where we find that by modulating the substrate, we can modify the reaction rate, the total yield from the reaction, and the speed of front propagation. These observations are confirmed in three numerical case studies involving the autocatalytic and bistable reactions on the torus and a sinusoidally-modulated substrate
One-Way Independent ANOVA There goes my hero

Children wearing superhero costumes are more likely to harm themselves because of the unrealistic impression of invincibility that these costumes could create: For example, children have reported to hospital with severe injuries because of trying ‘to initiate flight without having planned for landing strategies’ (Davies, Surridge, Hole, & MunroDavies, 2007). I can relate to the imagined power that a costume bestows upon you; even now, I have been known to dress up as Fisher by donning a beard and glasses and trailing a goat around on a lead in the hope that it might make me more knowledgeable about statistics. Imagine we had data about the severity of injury (on a scale from 0, no injury, to 100, death) for children reporting to the emergency centre at hospitals and information on which superhero costume they were wearing (hero): Spiderman, superman, the hulk or a teenage mutant ninja turtle. The Data are in Table 1 and there are descriptive statistics in Output 1. The researcher hypothesized: • Costumes of ‘flying’ superheroes (i.e. That is, the ones that travel through the air: Superman and Spiderman) will lead to more severe injuries than non-flying ones (the Hulk and Ninja Turtles). • There will be a diminishing trend in injuries depending on the costume: Superman (most injuries because he flies), Spiderman (next highest injuries because although technically he doesn’t fly, he does climb buildings and throws himself about high up in the air), Hulk (doesn’t tend to fly about in the air much but does smash buildings and punch hard objects that would damage a child if they hit them), and Ninja Turtles (let’s face it, they engage in fairly twee Ninja routines). Table 1: Data showing the severity of injury sustained by 30 children wearing superhero costumes Costume Injury
Vacuum drying of concentrated malta juice for production of malta powder using RSM

The malta powder was produced using a vacuum dryer under various drying conditions. Fresh concentrated malta juice was added with methyl cellulose, whole milk powder, tricalcium phosphate and glycerol monostearate at 0.08 to 0.016, 0.02 to 0.06, 0.0025 to 0.0045 and 0.005 to 0.015kg/kg of malta solid before exposing to the different drying temperatures at 65, 70, 75, 80, and 85°C in different time intervels as 0, 20, 60, 100, 140, 260, 380, 500, 620, 740 minutes. The drying rate of sample 24 was found higher due to added ingredients of methyl cellulose, tricalcium phosphate and glycerol monostearate. The different models were fied to the experimental data to predict the drying time, the generalized exponential model was found best, the predicted drying time at temperature (85°C) and EMC (1.49%db) was 322 minutes for the sample 24 to produce good quality malta powder.
Global Asymptotic Stability of PD Control for PM Stepper Motor Servo‐Systems

Commutation is a well‐known and successful strategy used in practice to control permanent magnet stepper motors. However, stability analysis has not been presented until now for this simple control strategy. In this note we prove, for the first time, that commutation achieves global asymptotic stability when used to regulate position in Euler–Lagrange systems actuated by permanent magnet stepper motors. Contrary to the traditional design methodology, this is accomplished by taking into account the electrical dynamics of the motors and, hence, we avoid the possibility of either performance degradation or instability due to the neglected electrical dynamics. We include high‐gain electric current loops and we introduce a saturated output feedback PD controller as the desired torque, i.e. velocity measurements are not required.
Higher-order topology induced by structural buckling

Abstract Higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, the physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry is preserved in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\beta $\end{document}-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.