Miracle-dz/UniFAR-FTUs huggingface dataset:
Topics in Extremal and Probabilistic Combinatorics

In this thesis, we consider a collection of problems in extremal and probabilistic combinatorics, specifically graph theory. First, we consider a close relative of the Cops and Robbers game called Revolutionaries and Spies, a two-player pursuit/evasion game devised by Beck to model network security. We show that on a ‘typical’ graph, if the second player has fewer pieces than are required to execute a particular trivial winning strategy, then the game is a first player win. Second, we consider the emergence of the square of a Hamilton cycle in a random geometric graph process, and show that typically, the exact instant at which a simple local obstacle is eliminated at every vertex, is the exact instant at which the graph becomes square Hamiltonian. This is in stark contrast to the ‘normal’ Erdős-Rényi random graph process, in which square Hamiltonicity is both not ‘local’ in this sense, and occurs only once the graph is reasonably dense. Finally, we study an extremal problem concerning tournaments, that of maximising the number of oriented cycles of a fixed length. A ‘folklore’ result states that for 3-cycles one cannot do significantly better than a random tournament. More recent work shows that same is true for 5-cycles, and perhaps surprisingly that this is not true for 4-cycles. We conjecture that one can significantly beat the random tournament in expectation if and only if the length of the cycle is divisible by four, proving the ‘if’ statement, as well as a variety of new cases of the ‘only if’ statement, including the case that the graph is sufficiently close to being regular.
A Review and Application of the Finite-Difference Time-Domain Algorithm Applied to the Schrodinger Equation

This paper contains a review of the FDTD algorithm as applied to the time-dependent Schrödinger equation, and the basic update equations are derived in their standard form. A simple absorbing boundary condition is formulated and shown to be effective with narrowband wave functions. The stability criterion is derived from a simple, novel perspective and found to give better efficiency than earlier attempts. Finally, the idea of probability current is introduced for the first time and shown how it can be used to radiate new probability into a simulation domain. This removes the need to define an initial-valued wave function, and the concept is demonstrated by measuring the transmission coefficient through a potential barrier.
ASSOCIATION OF CHANGES IN SPATIOTEMPORAL VARIABLES AT EACH STEP WITH 100-M SPRINT PERFORMANCE IN PREADOLESCENT SPRINTERS

The purpose of this study was to investigate the association of acceleration and changes in spatiotemporal variables at each step with 100 m sprint performance in preadolescent sprinters. Twenty-six boys performed 100 m sprints, and their spatiotemporal variables were measured at each step. Acceleration was negatively correlated with the 100m sprint time from the 1st to 21st step. The rates of change in step frequency were positively correlated with acceleration at the 2nd and 3rd step. Aftter the 3rd step, rates of change in step length were positively correlated with acceleration. The acceleration caused by increase in step frequency and step length up to reaching to the maximal sprint velocity is effective for improving the 100 m sprint time in preadolescent sprinters.
TODA FIELD THEORIES ASSOCIATED WITH HYPERBOLIC KAC-MOODY ALGEBRA — PAINLEVÉ PROPERTIES AND W ALGEBRAS

We show that the Painleve test is useful not only for probing (non)integrability but also for finding the values of spins of conserved currents (W currents) in Toda field theories (TFT’s). In the case of TFT’s based on simple Lie algebras the locations of resonances are shown to give precisely the spins of conserved W currents. We apply this test to TFT’s based strictly on hyperbolic Kac-Moody algebras and show that there exist no resonance other than that at n = 2, which corresponds to the energy-momentum tensor, indicating their nonintegrability. We also check by direct calculation that there are no spin-3 or -4 conserved currents for all the hyperbolic TFT’s in agreement with the result of our Painleve analysis.
Communication System Security

Helping current and future system designers take a more productive approach in the field, Communication System Security shows how to apply security principles to state-of-the-art communication systems. The authors use previous design failures and security flaws to explain common pitfalls in security design. Divided into four parts, the book begins with the necessary background on practical cryptography primitives. This part describes pseudorandom sequence generators, stream and block ciphers, hash functions, and public-key cryptographic algorithms. The second part covers security infrastructure support and the main subroutine designs for establishing protected communications. The authors illustrate design principles through network security protocols, including transport layer security (TLS), Internet security protocols (IPsec), the secure shell (SSH), and cellular solutions. Taking an evolutionary approach to security in todays telecommunication networks, the third part discusses general access authentication protocols, the protocols used for UMTS/LTE, the protocols specified in IETF, and the wireless-specific protection mechanisms for the air link of UMTS/LTE and IEEE 802.11. It also covers key establishment and authentication in broadcast and multicast scenarios. Moving on to system security, the last part introduces the principles and practice of a trusted platform for communication devices. The authors detail physical-layer security as well as spread-spectrum techniques for anti-jamming attacks. With much of the material used by the authors in their courses and drawn from their industry experiences, this book is appropriate for a wide audience, from engineering, computer science, and mathematics students to engineers, designers, and computer scientists. Illustrating security principles with existing protocols, the text helps readers understand the principles and practice of security analysis.
P-FPT algorithms for bounded clique-width graphs

Recently, hardness results for problems in P were achieved using reasonable complexity theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these assumptions, many graph theoretic problems do not admit truly subquadratic algorithms. A central technique used to tackle the difficulty of the above mentioned problems is fixed-parameter algorithms with polynomial dependency in the fixed parameter (P-FPT). Applying this technique to clique-width, an important graph parameter, remained to be done. In this paper we study several graph theoretic problems for which hardness results exist such as cycle problems, distance problems and maximum matching. We give hardness results and P-FPT algorithms, using clique-width and some of its upper bounds as parameters. We believe that our most important result is an algorithm in $O(k^4 · n + m)$-time for computing a maximum matching where $k$ is either the modular-width of the graph or the $P_4$-sparseness. The latter generalizes many algorithms that have been introduced so far for specific subclasses such as cographs. Our algorithms are based on preprocessing methods using modular decomposition and split decomposition. Thus they can also be generalized to some graph classes with unbounded clique-width.
Analogue model for anti-de Sitter as a description of point sources in fluids

We introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of motion satisfied by sound waves is the wave equation on $AdS_2\times S^1$. Since this spacetime is not globally hyperbolic, the dynamics of the Klein-Gordon field is not well defined until boundary conditions at the spatial boundary of $AdS_2$ are prescribed. On the analogue model end, those extra boundary conditions provide an effective description of the point source at $r=0$. For waves with circular symmetry, we relate the different physical evolutions to the phase difference between ingoing and outgoing scattered waves. We also show that the fluid configuration can be stable or unstable depending on the chosen boundary condition.
On the logarithmic Keller-Segel-Fisher/KPP system

We consider the Cauchy problem of a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. We study the global well-posedness, long-time behavior, vanishing coefficient limit and decay rate of solutions in \begin{document}$ \mathbb{R} $\end{document} . By utilizing energy methods, we show that for any given classical initial datum which is a perturbation around a constant equilibrium state with finite energy (not small), there exists a unique global-in-time solution to the Cauchy problem, and the solution converges to the constant equilibrium state, as time goes to infinity. Under the same initial condition, it is shown that the solution with positive chemical diffusion coefficient converges to the solution with zero chemical diffusion coefficient, as the coefficient goes to zero. Furthermore, for a slightly smaller class of initial data, we identify the algebraic decay rates of the solution to the constant equilibrium state by employing time-weighted energy estimates.
UNSHIFTED METASTABLE He i* MINI-BROAD ABSORPTION LINE SYSTEM IN THE NARROW-LINE TYPE 1 QUASAR SDSS J080248.18+551328.9

We report the identification of an unusual absorption-line system in the quasar SDSS J080248.18+551328.9 and present a detailed study of the system, incorporating follow-up optical and near-IR spectroscopy. A few tens of absorption lines are detected, including He i*, Fe ii*, and Ni ii*, which arise from metastable or excited levels, as well as resonant lines in Mg i, Mg ii, Fe ii, Mn ii, and Ca ii. All of the isolated absorption lines show the same profile of width Δv ∼ 1500 km s−1 centered at a common redshift as that of the quasar emission lines, such as [O ii], [S ii], and hydrogen Paschen and Balmer series. With narrow Balmer lines, strong optical Fe ii multiplets, and weak [O iii] doublets, its emission-line spectrum is typical for that of a narrow-line Seyfert 1 galaxy (NLS1). We have derived reliable measurements of the gas-phase column densities of the absorbing ions/levels. Photoionization modeling indicates that the absorber has a density of nH ∼ (1.0–2.5) × 105 cm−3 and a column density of NH ∼ (1.0–3.2) × 1021 cm−2 and is located at R ∼100–250 pc from the central supermassive black hole. The location of the absorber, the symmetric profile of the absorption lines, and the coincidence of the absorption- and emission-line centroid jointly suggest that the absorption gas originates from the host galaxy and is plausibly accelerated by stellar processes, such as stellar winds and/or supernova explosions. The implications for the detection of such a peculiar absorption-line system in an NLS1 are discussed in the context of coevolution between supermassive black hole growth and host galaxy buildup.
THE OUTCOME OF SUPERNOVAE IN MASSIVE BINARIES; REMOVED MASS, AND ITS SEPARATION DEPENDENCE

The majority of massive stars are formed in binary systems. It is hence reasonable to expect that most core-collapse supernovae (CCSNe) take place in binaries and the existence of a companion star may leave some imprints in observed features. Having this in mind, we have conducted two-dimensional hydrodynamical simulations of the collisions of CCSNe ejecta with the companion star in an almost-equal-mass (∼10 M☉) binary to find out possible consequences of such events. In particular we pay attention to the amount of mass removed and its dependence on the binary separation. In contrast to the previous surmise, we find that the companion mass is stripped not by momentum transfer but by shock heating. Up to 25% of the original mass can be removed for the closest separations and the removed mass decreases as Mub∝a−4.3 with the binary separation a. By performing some experimental computations with artificially modified densities of incident ejecta, we show that if the velocity of ejecta is fixed, the density of incident ejecta is the single important parameter that actually determines the removed mass as . On the other hand, another set of simulations with modified velocities of incident ejecta demonstrate that the strength of the forward shock, which heats up the stellar material and causes the mass loss of the companion star, is actually the key parameter for the removed mass.
Non-equilibrium chemistry and cooling in the diffuse interstellar medium – II. Shielded gas

We extend the non-equilibrium model for the chemical and thermal evolution of diuse interstellar gas presented in Richings et al. (2014) to account for shielding from the UV radiation eld. We attenuate the photochemical rates by dust and by gas, including absorption by Hi, H2, Hei, Heii and CO where appropriate. We then use this model to investigate the dominant cooling and heating processes in interstellar gas as it becomes shielded from the UV radiation. We consider a one-dimensional plane-parallel slab of gas irradiated by the interstellar radiation eld, either at constant density and temperature or in thermal and pressure equilibrium. The dominant thermal processes tend to form three distinct regions in the clouds. At low column densities cooling is dominated by ionised metals such as Siii, Feii, Feiii and Cii, which are balanced by photoheating, primarily from Hi. Once the hydrogen-ionising radiation becomes attenuated by neutral hydrogen, photoelectric dust heating dominates, while Cii becomes dominant for cooling. Finally, dust shielding triggers the formation of CO and suppresses photoelectric heating. The dominant coolants in this fully shielded region are H2 and CO. The column density of the Hi-H2 transition predicted by our model is lower at higher density (or at higher pressure for gas clouds in pressure equilibrium) and at higher metallicity, in agreement with previous PDR models. We also compare the Hi-H2 transition in our model to two prescriptions for molecular hydrogen formation that have been implemented in hydrodynamic simulations.
Fast and Efficient Limited Data Hyperspectral Remote Sensing Image Classification via GMM-Based Synthetic Samples

In hyperspectral remote sensing (HSRS), feature data can potentially become very high dimensional. At the same time, manual labeling of that data is an expensive task. As a consequence of these two factors, one of the core challenges is to perform multi-class classification using only relatively few training data points. In this work, we investigate the classification performance with limited training data. First, we revisit the optimization of the internal parameters of a classifier in the context of limited training data. Second, we report an interesting alternative to parameter optimization: classification performance can also be considerably increased by adding synthetic GMM data to the feature space while using a classifier with unoptimized parameters. Third, we show that using variational expectation maximization, we can achieve a much faster convergence in fitting the GMM on the data. In our experiments, we show that the addition of synthetic samples leads to comparable, and, in some cases, even higher classification performance than that for a properly tuned classifier on limited training data. One advantage of the proposed framework is that the reported performance improvements are achieved by a quite simple model. Another advantage is that this approach is computationally much more efficient than classifier parameter optimization and conventional expectation maximization.
Vortex-type elastic structured media and dynamic shielding

The paper presents an approach to modelling a novel elastic metamaterial structure that possesses non-trivial dispersion features. A system of spinners has been embedded into a two-dimensional periodic lattice system. The analysis of the motion of the spinners is used to derive an expression for a ‘chiral term’ in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortex-type nature of the structured media. The related effective behaviour in a continuous medium is implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.
Deep high-resolution X-ray spectra from cool-core clusters

We examine deep XMM-Newton Reflection Grating Spectrometer (RGS) spectra from the cores of three X-ray bright cool-core galaxy clusters, Abell 262, Abell 3581 and HCG 62. Each of the RGS spectra shows Fe XVII emission lines indicating the presence of gas around 0.5 keV. There is no evidence for O VII emission which would imply gas at still cooler temperatures. The range in detected gas temperature in these objects is a factor of 3.7, 5.6 and 2 for Abell 262, Abell 3581 and HCG 62, respectively. The coolest detected gas only has a volume filling fraction of 6 and 3 per cent for Abell 262 and Abell 3581, but is likely to be volume filling in HCG 62. Chandra spatially resolved spectroscopy confirms the low volume filling fractions of the cool gas in Abell 262 and Abell 3581, indicating this cool gas exists as cold blobs. Any volume heating mechanism aiming to prevent cooling would overheat the surroundings of the cool gas by a factor of 4. If the gas is radiatively cooling below 0.5 keV, it is cooling at a rate at least an order of magnitude below that at higher temperatures in Abell 262 and Abell 3581 and two orders of magnitude lower in HCG 62. The gas may be cooling non-radiatively through mixing in these cool blobs, where the energy released by cooling is emitted in the infrared. We find very good agreement between smooth particle inference modelling of the cluster and conventional spectral fitting. Comparing the temperature distribution from this analysis with that expected in a cooling flow, there appears to be an even larger break below 0.5 keV as compared with previous empirical descriptions of the deviations of cooling flow models.
Will There Be Future Deceleration? A Study of Particle Creation Mechanism in Nonequilibrium Thermodynamics

The paper deals with nonequilibrium thermodynamics based on adiabatic particle creation mechanism with the motivation of considering it as an alternative choice to explain the recent observed accelerating phase of the universe. Using Friedmann’s equations, it is shown that the deceleration parameter () can be obtained from the knowledge of the particle production rate (). Motivated by thermodynamical point of view, cosmological solutions are evaluated for the particle creation rates in three cosmic phases, namely, inflation, matter dominated era, and present late time acceleration. The deceleration parameter () is expressed as a function of the redshift parameter (), and its variation is presented graphically. Also, statefinder analysis has been presented graphically in three different phases of the universe. Finally, two noninteracting fluids with different particle creation rates are considered as cosmic substratum, and deceleration parameter () is evaluated. Whether more than one transition of is possible or not is examined by graphical representations.
On the proximity of multiplicative functions to the function counting prime factors with multiplicity

We examine how closely a multiplicative function resembles an additive function. Given a multiplicative function $g$ and an additive function $f$, we examine the size of the quantity $E(f,g;x)=\# \{n\leq x:f(n)=g(n)\}$. We establish a lower bound for $E(\Omega,g,x)$.
Missing Data in Complex Sample Surveys: Impact of Deletion and Imputation Treatments on Point and Interval Parameter Estimates

viii CHAPTER ONE: INTRODUCTION . 1 Background . 1 Summary . 7 Research Questions . 8 Limitations and Delimitations . 9 Definitions of Frequently Used Terms . 10 CHAPTER TWO: LITERATURE REVIEW . 13 Complex Sample Surveys . 13 Sample Weights . 15 Variance Estimation . 16 Missing Data Mechanisms . 18 MCAR. 19 MAR. . 20 MNAR. 20 Missing Data Treatment Methods . 22 Listwise Deletion. 23 Hot-Deck Imputation. 26 Regression Imputation. 31 Multiple Imputation. 34 Past Studies. 40
Intra-day optical multi-band quasi-simultaneous observation of BL Lacertae object S5 0716+714 from 2013 to 2016

We perform quasi-simultaneous optical multi-band monitoring of BL Lac object S5 0716+714 on seven nights from 2013 to 2016. Intra-day variability (IDV) is found on all seven nights. The source was faintest on JD 2456322 with 14.15 mags and brightest on JD 2457437 with 12.51 mags in the $R$ band. The maximum intra-day variation we observed is 0.15 mags in the $B$ band on JD 2456322. Both bluer-when-brighter and achromatic spectral behaviours were observed on the intra-day timescale. On the longer-term scale, the object exhibited a mild bluer-when-brighter behaviour between the $B$ and $R$ bands. We estimate the inter-band lags using two independent methods. The variation in the $B$ band was observed to lag that in the $I$ band by about 15 minutes on JD 2457315. We compare this lag with one reported previously and discussed the origin of these lags.
A NEW MEASUREMENT OF THE BULK FLOW OF X-RAY LUMINOUS CLUSTERS OF GALAXIES

We present new measurements of the large-scale bulk flows of galaxy clusters based on five-year WMAP data and a significantly expanded X-ray cluster catalog. Our method probes the flow via measurements of the kinematic Sunyaev–Zel'dovich (SZ) effect produced by the hot gas in moving clusters. It computes the dipole in the cosmic microwave background data at cluster pixels, which preserves the SZ component while integrating down other contributions. Our improved catalog of over 1000 clusters enables us to further investigate possible systematic effects and, thanks to a higher median cluster redshift, allows us to measure the bulk flow to larger scales. We present a corrected error treatment and demonstrate that the more X-ray luminous clusters, while fewer in number, have much larger optical depth, resulting in a higher dipole and thus a more accurate flow measurement. This results in the observed correlation of the dipole derived at the aperture of zero monopole with the monopole measured over the cluster central regions. This correlation is expected if the dipole is produced by the SZ effect and cannot be caused by unidentified systematics (or primary cosmic microwave background anisotropies). We measure that the flow is consistent with approximately constant velocity out to at least ≃800 Mpc. The significance of the measured signal peaks around 500 h−170 Mpc, most likely because the contribution from more distant clusters becomes progressively more diluted by the WMAP beam. However, at present, we cannot rule out that these more distant clusters simply contribute less to the overall motion.