Miracle-dz/UniFAR-FTUs huggingface dataset:
Impact of tides on the transit-timing fits to the TRAPPIST-1 system

Transit timing variations (TTVs) can be a very efficient way of constraining masses and eccentricities of multi-planet systems. Recent measurements of the TTVs of TRAPPIST-1 have led to an estimate of the masses of the planets, enabling an estimate of their densities and their water content. A recent TTV analysis using data obtained in the past two years yields a 34 and 13% increase in mass for TRAPPIST-1b and c, respectively. In most studies to date, a Newtonian N-body model is used to fit the masses of the planets, while sometimes general relativity is accounted for. Using the Posidonius N-body code, in this paper we show that in the case of the TRAPPIST-1 system, non-Newtonian effects might also be relevant to correctly model the dynamics of the system and the resulting TTVs. In particular, using standard values of the tidal Love number k2 (accounting for the tidal deformation) and the fluid Love number k2f (accounting for the rotational flattening) leads to differences in the TTVs of TRAPPIST-1b and c that are similar to the differences caused by general relativity. We also show that relaxing the values of tidal Love number k2 and the fluid Love number k2f can lead to TTVs which differ by as much as a few 10 s on a 3−4-yr timescale, which is a potentially observable level. The high values of the Love numbers needed to reach observable levels for the TTVs could be achieved for planets with a liquid ocean, which if detected might then be interpreted as a sign that TRAPPIST-1b and TRAPPIST-1c could have a liquid magma ocean. For TRAPPIST-1 and similar systems the models to fit the TTVs should potentially account for general relativity, for the tidal deformation of the planets, for the rotational deformation of the planets, and to a lesser extent for the rotational deformation of the star, which would add up to 7 × 2 + 1 = 15 additional free parameters in the case of TRAPPIST-1.
Linear stability of the ITER 15 MA scenario against the alpha fishbone

The stability of the n = m = 1 alpha-fishbone kinetic-MHD mode on the ITER 15 MA baseline scenario (ITER Physics Expert Group on Energe Drive and ITER Physics Basis 1999 Nucl. Fusion 39 2471–95) is analyzed using the non-linear hybrid kinetic-MHD code XTOR-K. Quantitative agreement is found between the complex frequencies ω + iγ computed with the linear model in (Brochard G. et al 2018 J. Phys.: Conf. Series 1125 012003) and XTOR-K’s linear simulations. Identical precessional resonance positions in phase space are also found between the linear model and XTOR-K. Linear hybrid simulations performed with XTOR-K on the ITER 15 MA scenario reveal that this configuration is likely to be unstable against the alpha fishbone mode. The fishbone thresholds for kinetic-MHD equilibria with flat q profiles with on-axis safety factor just below unity lies between βα,thres/βtot=6−10%, whereas the expected beta ratio on ITER is βα/βtot=15−20% (ITER Physics Expert Group on Energe Drive and ITER Physics Basis 1999 Nucl. Fusion 39 2471–95).
Controllability Analysis and Optimal Control of Mixed Traffic Flow With Human-Driven and Autonomous Vehicles

Connected and automated vehicles (CAVs) have a great potential to improve traffic efficiency in mixed traffic systems, which has been demonstrated by multiple numerical simulations and field experiments. However, some fundamental properties of mixed traffic flow, including controllability and stabilizability, have not been well understood. This paper analyzes the controllability of mixed traffic systems and designs a system-level optimal control strategy. Using the Popov-Belevitch-Hautus (PBH) criterion, we prove for the first time that a ring-road mixed traffic system with one CAV and multiple heterogeneous human-driven vehicles is not completely controllable, but is stabilizable under a very mild condition. Then, we formulate the design of a system-level control strategy for the CAV as a structured optimal control problem, where the CAV’s communication ability is explicitly considered. Finally, we derive an upper bound for reachable traffic velocity via controlling the CAV. Extensive numerical experiments verify the effectiveness of our analytical results and the proposed control strategy. Our results validate the possibility of utilizing CAVs as mobile actuators to smooth traffic flow actively.
S62 on a 9.9 yr Orbit around SgrA*

We present the Keplerian orbit of S62 around the supermassive black hole Sagittarius A* (SgrA*) in the center of our Galaxy. We monitor this S-star cluster member over more than a full orbit around SgrA* using the Very Large Telescope with the near-infrared instruments Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) and NAOS+CONICA (NACO). For that, we are deriving positional information from deconvolved images. We apply the Lucy–Richardson algorithm to the data sets. The NACO observations cover data from 2002 to 2018, and the SINFONI data cover 2008–2012. S62 can be traced reliably in both data sets. Additionally, we adapt one KECK data point for 2019 that supports the reidentification of S62 after the pericenter passage of S2. With and a periapse velocity of approximately 10% of the speed of light, S62 has the shortest known stable orbit around the supermassive black hole in the center of our Galaxy to date. From the analysis, we also derive the enclosed mass from a maximum likelihood method to be 4.15 ± 0.6 × 106M⊙.
Almost Sure Convergence of Dropout Algorithms for Neural Networks

We investigate the convergence and convergence rate of stochastic training algorithms for Neural Networks (NNs) that, over the years, have spawned from Dropout (Hinton et al., 2012). Modeling that neurons in the brain may not fire, dropout algorithms consist in practice of multiplying the weight matrices of a NN component-wise by independently drawn random matrices with $\{0,1\}$-valued entries during each iteration of the Feedforward-Backpropagation algorithm. This paper presents a probability theoretical proof that for any NN topology and differentiable polynomially bounded activation functions, if we project the NN's weights into a compact set and use a dropout algorithm, then the weights converge to a unique stationary set of a projected system of Ordinary Differential Equations (ODEs). We also establish an upper bound on the rate of convergence of Gradient Descent (GD) on the limiting ODEs of dropout algorithms for arborescences (a class of trees) of arbitrary depth and with linear activation functions.
New Insights on One-Sided Lipschitz and Quadratically-Inner Bounded Nonlinear Dynamic Systems

Nonlinear dynamic systems can be classified into various classes depending on the modeled nonlinearity. These classes include Lipschitz, bounded Jacobian, one-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes essentially yield bounding constants characterizing the nonlinearity. This is then used to design observers and controllers through Riccati equations or matrix inequalities. While analytical expressions for bounding constants of Lipschitz and bounded Jacobian nonlinearity are studied in the literature, OSL and QIB classes are not thoroughly analyzed—computationally or analytically. In short, this paper develops analytical expressions of OSL and QIB bounding constants. These expressions are posed as constrained maximization problems, which can be solved via various optimization algorithms. This paper also presents a novel insight particularly on QIB function set: any function that is QIB turns out to be also Lipschitz continuous.
The Eisenstein ideal for weight k and a Bloch–Kato conjecture for tame families

We study the Eisenstein ideal for modular forms of even weight $k>2$ and prime level $N$. We pay special attention to the phenomenon of $\mathit{extra \ reducibility}$: the Eisenstein ideal is strictly larger than the ideal cutting out reducible Galois representations. We prove a modularity theorem for these extra reducible representations. As consequences, we relate the derivative of a Mazur-Tate $L$-function to the rank of the Hecke algebra, generalizing a theorem of Merel, and give a new proof of a special case of an equivariant main conjecture of Kato. In the second half of the paper, we recall Kato's formulation of this main conjecture in the case of a family of motives given by twists by characters of conductor $N$ and $p$-power order and its relation to other formulations of the equivariant main conjecture.
Minimizing Dynamic Regret and Adaptive Regret Simultaneously

Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regret and adaptive regret have been proposed to guide the design of online algorithms. The former one aims to minimize the global regret with respect to a sequence of changing comparators, and the latter one attempts to minimize every local regret with respect to a fixed comparator. Existing algorithms for dynamic regret and adaptive regret are developed independently, and only target one performance measure. In this paper, we bridge this gap by proposing novel online algorithms that are able to minimize the dynamic regret and adaptive regret simultaneously. In fact, our theoretical guarantee is even stronger in the sense that one algorithm is able to minimize the dynamic regret over any interval.
Time-dependence in non-Hermitian quantum systems

In this thesis we present a coherent and consistent framework for explicit time-dependence in non-Hermitian quantum mechanics. The area of non-Hermitian quantum mechanics has been growing rapidly over the past twenty years [2]. This has been driven by the fact that PT -symmetric non-Hermitian systems exhibit real energy eigenvalues and unitary time evolution [1, 3, 4]. Historically, the introduction of time into the world of non-Hermitian quantum mechanics has been a conceptually difficult problem to address [5, 6], as it requires the Hamiltonian to become unobservable. However, we solve this issue with the introduction of a new observable energy operator [7]. We explain why its instigation is a necessary and natural progression in this setting. For the first time, the introduction of time has allowed us to make sense of the parameter regime in which the PT -symmetry is spontaneously broken. Ordinarily, in the time-independent setting, the energy eigenvalues become complex and the wave functions are asymptotically unbounded. However, we demonstrate that in the time-independent setting this broken symmetry can be mended and analysis on the spontaneously broken PT regime is indeed possible. We provide many examples of this mending on a wide range of different systems, beginning with a 2 x 2 matrix model [8] and extending to higher dimensional matrix models [9] and coupled harmonic oscillator systems with infinite Hilbert space [10, 11]. Furthermore, we use the framework to perform analysis on time-dependent quasi-exactly solvable models [12]. The ability to make sense of the spontaneously broken PT regime has revealed a vast array of new and exotic effects. We present the "eternal life" of entropy [13] in this thesis. Ordinarily, for entangled quantum systems coupled to the environments, the entropy decays rapidly to zero. However, in the spontaneously broken regime, we find the entropy decays asymptotically to a non-zero value. Finally, we create an elegant framework for Darboux and Darboux/Crum transformations for time-dependent non-Hermitian Hamiltonians [14]. This combines the area of non-Hermitian quantum mechanics with non linear differential equations and solitons.
Use of Space and Its Relationship with Sex, Body Size, and Color Polymorphism in Liolaemus xanthoviridis (Iguania: Liolaemini) in Patagonia

Abstract. The local spatial distribution of individual animals is often described in terms of home range (HR), whereas territory traditionally refers to an area defended for exclusive use. The size of the HR is considered an important indicator of the behavioral characteristics of an animal, and it can be influenced by factors such as sex, body size, population density, and social behavior. In polymorphic species, morphs may differ in space use, and they may be characterized by different reproductive strategies. The aim of this study is to quantify space use in a population of the lizard Liolaemus xanthoviridis (Iguania: Liolaemini) and its relationship with body size, sex, and color polymorphism. At a single locality in Argentina (Bahía Isla Escondida, Chubut), over four summer seasons (2012–2015) we marked 156 lizards and recorded body measurements, sex, dorsal and ventral color patterns, and the spatial location of each individual. Our results showed that HR size differed significantly between sexes and was significantly associated with body sizes in males, but not with dorsal coloration and ventral melanism. Moreover, males of L. xanthoviridis have a high percentage of overlap in their HRs. The absence of a relationship between HR size and dorsal coloration or ventral melanism suggests the absence of multiple reproductive strategies within each sex. Because females of L. xanthoviridis seem to be territorial, but not males, we propose that they may be interacting in a system of dominance hierarchies, a hypothesis that needs behavioral testing.
Student Teachers’ Perception on Blended Learning in an In-Service Teacher Training Programme: A Case Study at Teacher Education Institute Batu Lintang Campus

The study aimed to reveal how blended learning was perceived by a group of student teachers enrolled an in-service teacher training course. A survey using google forms was used to collect data for the study. The research instrument, included nine components of blended learning. A total of 179 student teachers, who were pursuing their Postgraduate Diploma in Education (PDPP), took part in the study. The findings of the study revealed that among the nine components of blended learning, the role of the teacher/lecturer and face to face lessons were the two most important components perceived by student teachers. The third component was role of students in participating in online discussions. Student teachers also revealed they needed to interact with other students, both online and face to face. Any LMS could be accepted in blended learning programmes but ease of use features were perceived to be important to enable them to participate in online discussions and to receive feedback. However, their participation online must be considered as part of their overall course assessment. Attractiveness of the online materials and online sharing of unrelated course materials were perceived as insignificant. Based on the findings, implications and recommendations for future research were also included in the report.
A group theoretic proof of Frobenius' theorem

Let G be a Frobenius group with the Frobenius kernel N. Applying character theory, G. Frobenius proved that N was a normal subgroup of G in the year 1901. This is a celebrated application of the character theory of finite groups. In the note, we give a character-free proof of this result, which is a well-known problem in the theory of finite groups.
Intermittent planet migration and the formation of multiple dust rings and gaps in protoplanetary discs

A key challenge for protoplanetary disks and planet formation models is to be able to make a reliable connection between observed structures in the disks emission, like bright and dark rings or asymmetries, and the supposed existence of planets triggering these structures. The observation of N dark rings of emission is often interpreted as evidence for the presence of N planets which clear dust gaps around their orbit and form dust-trapping pressure maxima in the disk. The vast majority of the models that studied the impact of planets on the dynamics of dust and gas in a protoplanetary disk assumed planets on fixed orbits. Here we go a different route and examine how the large-scale inward migration of a single planet structures the dust content of a massive disk. In many circumstances, the migration of a partial gap-opening planet with a mass comparable to Saturn is found to run away intermittently. By means of 2D gas and dust hydrodynamical simulations, we show that intermittent runaway migration can form multiple dust rings and gaps across the disk. Each time migration slows down, a pressure maximum forms beyond the planet gap that traps the large dust. Post-processing of our simulations results with 3D dust radiative transfer calculations confirms that intermittent runaway migration can lead to the formation of multiple sets of bright and dark rings of continuum emission in the (sub)millimeter beyond the planet location.
Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization

We consider the problem of maximizing a non-concave Lipschitz multivariate function f over a compact domain. We provide regret guarantees (i.e., optimization error bounds) for a very natural algorithm originally designed by Piyavskii and Shubert in 1972. Our results hold in a general setting in which values of f can only be accessed approximately. In particular, they yield state-of-the-art regret bounds both when f is observed exactly and when evaluations are perturbed by an independent subgaussian noise.
Equivariant K-Theory and Tangent Spaces to Schubert Varieties

Tangent spaces to Schubert varieties of type A were characterized by Lakshmibai and Seshadri. This result was extended to the other classical types by Lakshmibai. We give a uniform characterization of tangent spaces to Schubert varieties in cominuscule G/P. Our results extend beyond cominuscule G/P; they describe the tangent space to any Schubert variety in G/B at a point xB, where x is a cominuscule Weyl group element in the sense of Peterson. Our results also give partial information about the tangent space to any Schubert variety at any point. Our method is to describe the tangent spaces of Kazhdan-Lusztig varieties, and then recover results for Schubert varieties. Our proof uses a relationship between weights of the tangent space of a variety with torus action, and factors of the class of the variety in torus equivariant K-theory. The proof relies on a formula for Schubert classes in equivariant K-theory due to Graham and Willems, as well as a theorem on subword complexes due to Knutson and Miller.
Global Convergence of Frank Wolfe on One Hidden Layer Networks

We derive global convergence bounds for the Frank Wolfe algorithm when training one hidden layer neural networks. When using the ReLU activation function, and under tractable preconditioning assumptions on the sample data set, the linear minimization oracle used to incrementally form the solution can be solved explicitly as a second order cone program. The classical Frank Wolfe algorithm then converges with rate $O(1/T)$ where $T$ is both the number of neurons and the number of calls to the oracle.
Attosecond Molecular Spectroscopy and Dynamics

The present review addresses the technical advances and the theoretical developments to realize and rationalize attosecond-science experiments that reveal a new dynamical time scale ($10^{-15}$-$10^{-18}$ s), with a particular emphasis on molecular systems and the implications of attosecond processes for chemical dynamics. After a brief outline of the theoretical framework for treating non-perturbative phenomena in Section 2, we introduce the physical mechanisms underlying high-harmonic generation and attosecond technology. The relevant technological developments and experimental schemes are covered in Section 3. Throughout the remainder of the chapter, we report on selected applications in molecular attosecond physics, thereby addressing specific phenomena mediated by purely electronic dynamics: charge localization in molecular hydrogen, charge migration in biorelevant molecules, high-harmonic spectroscopy, and delays in molecular photoionization.
The principal p ‐blocks with four irreducible characters

For a prime p , we determine a Sylow p ‐subgroup D of a finite group G such that the principal p ‐block B of G has four irreducible ordinary characters. It has been determined already for the cases where the number is up to three by work by R. Brauer, J. Brandt, and V.A. Belonogov 30 years ago. Our proof relies on the classification of finite simple groups.
Near-optimal Reinforcement Learning in Factored MDPs: Oracle-Efficient Algorithms for the Non-episodic Setting

We study reinforcement learning in factored Markov decision processes (FMDPs) in the non-episodic setting. We focus on regret analyses providing both upper and lower bounds. We propose two near-optimal and oracle-efficient algorithms for FMDPs. Assuming oracle access to an FMDP planner, they enjoy a Bayesian and a frequentist regret bound respectively, both of which reduce to the near-optimal bound $\widetilde{O}(DS\sqrt{AT})$ for standard non-factored MDPs. Our lower bound depends on the span of the bias vector rather than the diameter $D$ and we show via a simple Cartesian product construction that FMDPs with a bounded span can have an arbitrarily large diameter, which suggests that bounds with a dependence on diameter can be extremely loose. We, therefore, propose another algorithm that only depends on span but relies on a computationally stronger oracle. Our algorithms outperform the previous near-optimal algorithms on computer network administrator simulations.
Robust k-means Clustering for Distributions with Two Moments

We consider the robust algorithms for the $k$-means clustering problem where a quantizer is constructed based on $N$ independent observations. Our main results are median of means based non-asymptotic excess distortion bounds that hold under the two bounded moments assumption in a general separable Hilbert space. In particular, our results extend the renowned asymptotic result of Pollard, 1981 who showed that the existence of two moments is sufficient for strong consistency of an empirically optimal quantizer in $\mathbb{R}^d$. In a special case of clustering in $\mathbb{R}^d$, under two bounded moments, we prove matching (up to constant factors) non-asymptotic upper and lower bounds on the excess distortion, which depend on the probability mass of the lightest cluster of an optimal quantizer. Our bounds have the sub-Gaussian form, and the proofs are based on the versions of uniform bounds for robust mean estimators.