Miracle-dz/UniFAR-FTUs huggingface dataset:
Efficiently Learning Human Preferences for Robot Autonomy

approved: Geoffrey A. Hollinger Human-robot teams are invaluable for mapping unknown environments, exploring difficultto-reach areas, and manipulating inaccessible equipment. However, guiding autonomous robots requires dealing with these dynamic domains while synthesizing a significant amount of data and balancing competing objectives. Current mission planning methods often involve manually specifying low-level parameters of the mission, such as exact waypoints or control inputs. These methods cannot perfectly cope with the changing surroundings and limited communications that come with operating in these complex conditions. To address this and reduce the burden on human operators, the field has trended towards ever-increasing levels of autonomy. Providing this long-term autonomy requires more usable, robust collaborative mission planning solutions that leverage the strengths of both the robot and the human operator. In this thesis, we propose two novel methods for improving the collaboration of humanrobot teams by enabling the robot to learn an operator’s preferences for mission planning. These techniques provide the robot with a rich representation of the human’s goals while utilizing familiar techniques to speed learning. The first method is trained by making smallscale, iterative improvements to candidate mission plans generated by the robot, similar to the small improvements an operator would make while planning an actual mission. Using a novel coactive learning algorithm, the method learns the operator’s preferences from the feature differences between the original and improved mission plans while remaining robust to errors and noise in the operator’s corrections. The second proposed method simplifies the queries by asking survey-style rating and ranking questions about candidate plans. These queries are generated by a Gaussian process (GP) active learner that uses the responses to learn the most preferred region of the mission preference space. The ranking query responses provide the GP with general relational information about several points in the preference space, while the rating query responses provide a specific preference about a single point. A custom probit allows the GP to incorporate the different strengths of each query type into a single preference model. Tests in simulated lake monitoring missions show that these methods can efficiently and accurately learn an operator’s preferences. Additionally, a field trial in which an EcoMapper autonomous underwater vehicle monitors the ecology of a lake validates the use of the coactive learning method. These results demonstrate that these techniques can enable a robot to accurately learn a human operator’s preferences, then autonomously plan and perform missions that apply those preferences without relying on regular intervention by the operator. ©Copyright by Thane Somers June 1, 2022 All Rights Reserved Efficiently Learning Human Preferences for Robot Autonomy
Generalised Mathieu Moonshine

The Mathieu twisted twining genera, i.e. the analogues of Norton's generalised Moonshine functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the expected consistency conditions, and that their behaviour under modular transformations is controlled by a 3-cocycle in H^3(M_24,U(1)), just as for the case of holomorphic orbifolds. This suggests that a holomorphic VOA may be underlying Mathieu Moonshine.
Randomized and Robust Methods for Uncertain Systems using R-RoMulOC, with Applications to DEMETER Satellite Benchmark

R-RoMulOC is a freely distributed toolbox aimed at making easily available to the users various optimization-based methods for dealing with uncertain systems. It implements both deterministic LMI-based results, which provide guaranteed performance for all values of the uncertainties, and probabilistic randomization-based approaches, which guarantee performance for all values of the uncertainties except for a subset with arbitrary small probability measure. The paper is devoted to the description of these two approaches for analysis and control design when applied to a satellite benchmark proposed by the CNES, the French Space Agency. The paper also describes the modeling of the DEMETER satellite and its integration into the R-RoMulOC toolbox as a challenging test example. Design of state-feedback controllers and closed-loop performance analysis are carried out with the randomized and robust methods available in the R-RoMulOC toolbox.
A combinatorial algorithm for constrained assortment optimization under nested logit model

We consider the assortment optimization problem with disjoint-cardinality constraints under two-level nested logit model. To solve this problem, we first identify a candidate set with $O(mn^2)$ assortments and show that at least one optimal assortment is included in this set. Based on this observation, a fast algorithm, which runs in $O(m n^2 \log mn)$ time, is proposed to find an optimal assortment.
Joint Pricing and Inventory Management with Regular and Expedited Supplies under Reference Price Eﬀects

Reference price eﬀects, as an important factor aﬀecting customers’ purchase decision for a certain commodity, has an signiﬁcant impact on the ﬁrms’ pricing and inventory strategies. Therefore, how to determine an appropriate sales pricing and order ﬂexibility strategy to maximize ﬁrms’ proﬁt is an essential task. A single-item, periodic-review ﬁnite horizon joint pricing and inventory system with regular and expedited supply sources under reference price eﬀects is investigated, where demand in consecutive periods are independent as well as price and reference price sensitive random variables. The optimal pricing and ordering strategies, and the impact of reference price eﬀects on these optimal decisions are studied. These results generalize those in Zhou and Chao (2014) in Production and Operations Management, Vol. 23, 65-80 to the reference price eﬀects. Moreover, the operational impact of adding reference price eﬀects is analyzed by comparing with their model. Finally, Numerical experiments characterize the qualitative properties of the optimal strategies and corresponding optimal proﬁt values under reference price eﬀects.
Time-Use and Subjective Well-Being: Is there a Preference for Activity Diversity?

Using the American and the French time-use surveys, we examine whether people have a preference for a more diversiﬁed mix of activities, in the sense that, everything else equal, they experience a higher level of well-being when their agenda is multi-activity, rather than concentrated on a very small number of activities. This could be due to decreasing marginal utility, as is assumed for the consumption of goods, if each episode of time is conceived as yielding a certain level of utility per se . However, in the presence of returns to specialization, people would face a trade-off between the efﬁciency of specialization and the taste for diversity, as concerns time arrangements. We test these hypotheses and investigate potential gender differences with regard to these patterns.
On spectral gap estimates of a Markov chain via hitting times and coupling

Well-known inequalities for the spectral gap of a discrete-time Markov chain, such as Poincaré's and Cheeger's inequalities, do not perform well if the transition graph of the Markov chain is strongly connected. For example in the case of nearest-neighbour random walk on the n-dimensional cube Poincaré's and Cheeger's inequalities are off by a factor n. Using a coupling technique and a contraction principle lower bounds on the spectral gap can be derived. Finally, we show that using the contraction principle yields a sharp estimate for nearest-neighbour random walk on the n-dimensional cube.
Computing the Nash solution for scheduling bargaining problems

In this paper we focus on the Nash Bargaining Solution (NBS) in a scheduling scenario with two players. The problem is shown to be NP-hard, but an effective computing scheme for finding NBS is presented. Extensive computational results are provided, showing that NBS can always be found within reasonable computation time.
On a quantitative reversal of Alexandrov’s inequality

Alexandrov’s inequalities imply that for any convex body A A , the sequence of intrinsic volumes V 1 ( A ) , … , V n ( A ) V_1(A),\ldots ,V_n(A) is non-increasing (when suitably normalized). Milman’s random version of Dvoretzky’s theorem shows that a large initial segment of this sequence is essentially constant, up to a critical parameter called the Dvoretzky number. We show that this near-constant behavior actually extends further, up to a different parameter associated with A A . This yields a new quantitative reverse inequality that sits between the approximate reverse Urysohn inequality, due to Figiel–Tomczak–Jaegermann and Pisier, and the sharp reverse Urysohn inequality for zonoids, due to Hug–Schneider. In fact, we study concentration properties of the volume radius and mean width of random projections of A A and show how these lead naturally to such reversals.
An optimal result for global existence and boundedness in a three-dimensional Keller-Segel(-Navier)-Stokes system (involving a tensor-valued sensitivity with saturation)

The coupled quasilinear Keller-Segel-Navier-Stokes system $$ \left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c),\quad x\in \Omega, t>0, c_t+u\cdot\nabla c=\Delta c-c+n,\quad x\in \Omega, t>0, u_t+\kappa(u \cdot \nabla)u+\nabla P=\Delta u+n\nabla \phi,\quad x\in \Omega, t>0, \nabla\cdot u=0,\quad x\in \Omega, t>0 \end{array}\right. \eqno(KSNF) $$ is considered under Neumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for $u$ in three-dimensional bounded domains $\Omega\subseteq \mathbb{R}^3$ with smooth boundary, where $\kappa\in \mathbb{R}$ is given constant, $\phi\in W^{1,\infty}(\Omega),m>0$, $|S(x,n,c)|\leq C_S(1+n)^{-\alpha}$ and the parameter $\alpha\geq0$. %For any small $\mu>0$, If $\alpha>\frac{1}{3}$, then for all reasonably regular initial data, a corresponding initial-boundary value problem for $(KSNF)$ possesses a globally defined weak solution. This result improves the result of Wang (Math. Models Methods Appl. Sci., 27(14):2745--2780, 2017), where the global {\bf very weak} solution for system $(KSNF)$ is obtained. Moreover, if $\kappa=0$ and $S(x,n,c)=C_S(1+n)^{-\alpha}$, then the system $(KSF)$ exists at least one global classical solution which is bounded in $\Omega\times(0,\infty)$. These results significantly improve or extend previous results of several authors. In comparison to the result for the corresponding fluid-free system, the {\bf optimal condition} on the parameter $\alpha$ for global (weak) existence and boundedness is obtained. Our proofs rely on Maximal Sobolev regularity techniques and on a variant of the natural gradient-like energy functional.
Topological groups of Kac-Moody type, Fuchsian twinnings and their lattices

This paper deals with a class of totally disconnected groups acting on buildings, among which are certain Kac-Moody groups. The apartments of our buildings are hyperbolic planes tiled by right-angled polygons. We discuss linearity properties for the groups, as well as an analogy with semisimple groups over local fields of positive characteristic. Looking for counter-examples to this analogy leads to the construction of Moufang twinnings "with several ground fields".
Highly ionized interstellar gas located in the Galactic disk and halo

High-resolution IUE absorption line spectra have been obtained for 40 distant stars in order to study the distribution of interstellar H I, Si IV, C IV, and N V in the Galactic disk and lower halo. Respective midplane densities of 2 x 10 to the -9th, 7 x 10 to the -9th, and 3 x 10 to the -9th are found for Si IV, C IV, and Ni V. Both column density and velocity data indicate that the highly ionized gas (HIG) is considerably more extended in directions away from the Galactic plane than is H I or Si II. The absorption-line velocities for the halo HIG are consistent with the notion that halo gas in the inner Galaxy rotates more slowly than gas in the underlying disk. The derived column densities suggest an exponential scale height for the HIG of about 3 kpc; however, a simple exponential distribution is a poor representation of the distribution of the gas. It is concluded that a full explanation of the origin of the halo HIG will probably require a blending of ideas from the Galactic fountain and the photoionized halo models.
Time evolution of the rule 150 cellular automaton activity from a Fibonacci iteration

The rule 150 cellular automaton is a remarkable discrete dynamical system, as it shows 1∕fα spectra if started from a single seed [J. Nagler and J. C. Claussen, Phys. Rev. E 71, 067103 (2005)]. Despite its simplicity, a feasible solution for its time behavior is not obvious. Its self-similarity does not follow a one-step iteration like other elementary cellular automata. Here it is shown how its time behavior can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length. This allows us to compute the total activity time series more efficiently than by simulating the whole spatiotemporal process or even by using the closed expression. The results are further extended to the generalization of rule 150 to the two-dimensional case and to Bethe lattices and the relation to corresponding integer sequences is discussed.
Burgess-like subconvexity for $\text{GL}_{1}$

We generalize our previous method on the subconvexity problem for $\text{GL}_{2}\times \text{GL}_{1}$ with cuspidal representations to Eisenstein series, and deduce a Burgess-like subconvex bound for Hecke characters, that is, the bound $|L(1/2,\unicode[STIX]{x1D712})|\ll _{\mathbf{F},\unicode[STIX]{x1D716}}\mathbf{C}(\unicode[STIX]{x1D712})^{1/4-(1-2\unicode[STIX]{x1D703})/16+\unicode[STIX]{x1D716}}$ for varying Hecke characters $\unicode[STIX]{x1D712}$ over a number field $\mathbf{F}$ with analytic conductor $\mathbf{C}(\unicode[STIX]{x1D712})$ . As a main tool, we apply the extended theory of regularized integrals due to Zagier developed in a previous paper to obtain the relevant triple product formulas of Eisenstein series.
Substrate design or reconstruction from free surface data for thin film flows

This paper addresses two inverse problems relevant to the flow of thin liquid films on uneven surfaces. The first one consists in controlling the free surface profile by a suitable design of the substrate and the second involves the reconstruction of the substrate topography from a known free surface profile. These problems are treated in the classical lubrication approximation framework and admit, for planar flows, a surprisingly simple close-form solution, which is successfully tested on a range of problems.
Aeronomy, a 20th Century emergent science: the role of solar Lyman series

Abstract. Aeronomy is, by definition, a multidisciplinary science which can be used to study the terrestrial atmosphere, as well as any planetary atmosphere and even the interplanetary space. It was officially recognized in 1954 by the International Union of Geodesy and Geophysics. The major objective of the present paper is to show how aeronomy developed since its infancy. The subject is so large that a guide-line has been chosen to see how aeronomy affects our atmospheric knowledge. This guideline is the solar Lyman alpha radiation which has different effects in the solar system. After a short description of the origins of aeronomy the first observations of this line are summarized since the beginning of the space age. Then the consequences of these observations are analyzed for the physics and chemistry of the neutral terrestrial atmosphere. New chemical processes had to be introduced, as well as new transport phenomena. Solar Lyman alpha also influences the structure of the Earth’s ionosphere, particularly the D-region. In the terrestrial exosphere, solar Lyman alpha scattered resonantly by atomic hydrogen is at present the only way to estimate this constituent in an almost collisionless medium. Since planetary atmospheres also contain atomic hydrogen, the Lyman alpha line has been used to deduce the abundance of this constituent. The same is true for the interplanetary space where Lyman alpha observations can be a good tool to determine the concentration. The last section of the paper presents a question which is intended to stimulate further research in aeronomy. Key words. Atmospheric composition and structure (middle atmosphere – composition and chemistry; thermosphere – composition and chemistry) – history of geophysics (atmospheric sciences)
RG Domain Walls and Hybrid Triangulations

This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find that we can build a variety of 3d theories that represent the local degrees of freedom at a given domain wall in various 4d duality frames, including both UV S-dual frames and IR Seiberg-Witten electric-magnetic dual frames. We pay special attention to Janus domain walls, defined by four-dimensional Lagrangians with position-dependent couplings. If the couplings on either side of the wall are weak in different UV duality frames, Janus domain walls reduce to S-duality walls, i.e. domain walls that encode the properties of UV dualities. If the couplings on one side are weak in the IR and on the other weak in the UV, Janus domain walls reduce to RG walls, i.e. domain walls that encode the properties of RG flows. We derive the 3d geometries associated to both types of domain wall, and test their properties in simple examples, both through basic field-theoretic considerations and via comparison with quantum Teichmuller theory. Our main mathematical tool is a parametrization and quantization of framed flat SL(K) connections on these geometries based on ideal triangulations.
Analyse statistique de quelques modèles de processus de type fractionnaire

Cette these porte sur l’analyse statistique de quelques modeles de processus stochastiques gouvernes par des bruits de type fractionnaire, en temps discret ou continu.Dans le Chapitre 1, nous etudions le probleme d’estimation par maximum de vraisemblance (EMV) des parametres d’un processus autoregressif d’ordre p (AR(p)) dirige par un bruit gaussien stationnaire, qui peut etre a longue memoire commele bruit gaussien fractionnaire. Nous donnons une formule explicite pour l’EMV et nous analysons ses proprietes asymptotiques. En fait, dans notre modele la fonction de covariance du bruit est supposee connue, mais le comportement asymptotique de l’estimateur (vitesse de convergence, information de Fisher) n’en depend pas.Le Chapitre 2 est consacre a la determination de l’entree optimale (d’un point de vue asymptotique) pour l’estimation du parametre de derive dans un processus d’Ornstein-Uhlenbeck fractionnaire partiellement observe mais controle. Nous exposons un principe de separation qui nous permet d’atteindre cet objectif. Les proprietes asymptotiques de l’EMV sont demontrees en utilisant le programme d’Ibragimov-Khasminskii et le calcul de transformees de Laplace d’une fonctionnellequadratique du processus.Dans le Chapitre 3, nous presentons une nouvelle approche pour etudier les proprietes du mouvement brownien fractionnaire melange et de modeles connexes, basee sur la theorie du filtrage des processus gaussiens. Les resultats mettent en lumiere la structure de semimartingale et menent a un certain nombre de proprietes d’absolue continuite utiles. Nous etablissons l’equivalence des mesures induites par le mouvement brownien fractionnaire melange avec une derive stochastique, et en deduisons l’expression correspondante de la derivee de Radon-Nikodym. Pour un indice de Hurst H > 3=4, nous obtenons une representation du mouvement brownien fractionnaire melange comme processus de type diffusion dans sa filtration naturelle et en deduisons une formule de la derivee de Radon-Nikodym par rapport a la mesurede Wiener. Pour H < 1=4, nous montrons l’equivalence de la mesure avec celle la composante fractionnaire et obtenons une formule pour la densite correspondante. Un domaine d’application potentielle est l’analyse statistique des modeles gouvernes par des bruits fractionnaires melanges. A titre d’exemple, nous considerons le modele de regression lineaire de base et montrons comment definir l’EMV et etudie son comportement asymptotique.
A Compactness Theorem for Embedded Measured Riemann Surface Laminations

We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$. To prove compactness result, we show that there is a suitable topology on the space of measured Riemann surface laminations induced by Levy-Prokhorov metric. As an application of the compactness theorem, we show that given a biholomorphism of $\phi $ of a closed complex manifold $X$, some power $\phi^k $ ($k>0$) fixes a measured Riemann surface lamination in $X$.
Generalized Mercer Kernels and Reproducing
 Kernel Banach Spaces

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First we verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, we develop a new concept of generalized Mercer kernels to construct $p$-norm RKBSs for $1\leq p\leq\infty$. The $p$-norm RKBSs preserve the same simple format as the Mercer representation of RKHSs. Moreover, the $p$-norm RKBSs are isometrically equivalent to the standard $p$-norm spaces of countable sequences. Hence, the $p$-norm RKBSs possess more geometrical structures than RKHSs including sparsity. The generalized Mercer kernels also cover many well-known kernels, for example, min kernels, Gaussian kernels, and power series kernels. Finally, we propose to solve the support vector machines in the $p$-norm RKBSs, which are to minimize the regularized empirical risks over the $p$-norm RKBSs. We show that the infinite dimensional support vector machines in the $p$-norm RKBSs can be equivalently transferred to finite dimensional convex optimization problems such that we obtain the finite dimensional representations of the support vector machine solutions for practical applications. In particular, we verify that some special support vector machines in the $1$-norm RKBSs are equivalent to the classical $1$-norm sparse regressions. This gives fundamental supports of a novel learning tool called sparse learning methods to be investigated in our next research project.
Symmetric forms for hyperbolic‐parabolic systems of multi‐gradient fluids

We consider multi‐gradient fluids endowed with a volume internal‐energy that is a function of mass density, volume entropy and their successive gradients. We obtain a thermodynamic form of the equation of motion and an equation of energy compatible with the two laws of thermodynamics. The equations of multi‐gradient fluids belong to the class of dispersive systems. In the conservative case, we can replace the set of equations by a quasi‐linear system written in a divergence form. Near an equilibrium position, we obtain a Hermitian‐symmetric system written in the form of Godunov's systems. Equilibrium positions are stable when the total volume energy of the fluid is a convex function of the conjugated variables ‐ called the main field ‐ of mass density, volume entropy, their successive gradients and velocity.