Analogue Of Space Research Articles

Speleology as an analogue to space exploration: The ESA CAVES training programme

Caves remain among the most challenging exploration frontiers on planet Earth. They are difficult to access, present a range of unique and unusual environmental characteristics, and can only be mapped through direct human exploration. These challenges and several environmental factors specific to caves mean that speleology shares several analogies with space missions. For humans, cave exploration imposes isolation, confinement, minimal privacy, technical challenges, limited equipment and supplies, a sense of disconnect from the surface and regular life, a lack of diurnal cycles, and the constant presence of risk. As many of the same challenges are imposed on humans during space exploration, in 2005 the European Space Agency (ESA) began examining the possibility of using natural cave systems as a platform for astronaut training. These efforts resulted in a new ESA training programme named CAVES (Cooperative Adventure for Valuing and Exercising human behaviour and performance Skills) being launched in 2011, involving astronauts from partner space agencies. The primary objective of this training is to enhance astronaut individual and team performance and behavioural competencies by exposing them to the challenges of a real mission into an unknown and dangerous environment. To achieve this, the course's training activities are based around a real scientific and technological programme focused on cave science. Many aspects of the location and course content have been designed by a team of behavioural experts, scientists, trainers, operations engineers and speleologists with the support of caving organizations and schools. CAVES training events leverage cave exploration to create situations that are analogues to spaceflight in terms of safety protocols, perception and management of risk, crew composition and role assignments, group living, isolation, and confinement. In addition, these courses provide an opportunity for astronauts to experience spaceflight-like or relevant operations, science, equipment testing, and exploration, in preparation for future planetary endeavours. The scientific, exploration and equipment testing aspects of the course are real (not simulated). This ensures that these activities provide benefits to the speleological and scientific communities, whilst guaranteeing the realism of these activities for training purposes. During six editions of CAVES, from 2011 to 2019, 34 astronauts from 6 different space agencies (ESA, NASA, JAXA, ROSCOSMOS, CSA and CNSA) have taken part in the training. The CAVES training programme has been recognized by all participant astronauts and, in particular, by those who have travelled to space, as one of the best space analogue training opportunities available on Earth. The learning outcomes are applicable to both current and future orbital missions, as well as surface and subsurface missions to other planetary bodies.

Noncommutative coordinate picture of the quantum phase space

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit coordinates and discuss the physical and dynamical picture. The isomorphism is then used as a base for the translation of the differential symplectic geometry of the infinite dimensional manifolds onto the observable algebra as a noncommutative geometry. Hence, we obtain the latter from the physical theory itself. We have essentially an extended formalism of the Schr̎odinger versus Heisenberg picture which we describe mathematically as like a coordinate map from the phase space, for which we have presented argument to be seen as the quantum model of the physical space, to the noncommutative geometry coordinated by the six position and momentum operators. The observable algebra is taken essentially as an algebra of formal functions on the latter operators. The work formulates the intuitive idea that the noncommutative geometry can be seen as an alternative, noncommutative coordinate, picture of familiar quantum phase space, at least so long as the symplectic geometry is concerned.

Quasi-inner functions and local factors

We introduce the notion of quasi-inner function and show that the product u=ρ∞∏ρv of m+1 ratios of local L-factors ρv(z)=γv(z)/γv(1−z) over a finite set F of places of Q inclusive of the archimedean place is quasi-inner on the left of the critical line ℜ(z)=12 in the following sense. The off diagonal part u21 of the matrix of the multiplication by u in the orthogonal decomposition of the Hilbert space L2 of square integrable functions on the critical line into the Hardy space H2 and its orthogonal complement is a compact operator. When interpreted on the unit disk, the quasi-inner condition means that the associated Haenkel matrix is compact. We show that none of the individual non-archimedean ratios ρv is quasi-inner and, in order to prove our main result we use Gauss multiplication theorem to factor the archimedean ratio ρ∞ into a product of m quasi-inner functions whose product with each ρv retains the property to be quasi-inner. Finally we prove that Sonin's space is simply the kernel of the diagonal part u22 for the quasi-inner function u=ρ∞, and when u(F)=∏v∈Fρv the kernels of the u(F)22 form an inductive system of infinite dimensional spaces which are the semi-local analogues of (classical) Sonin's spaces.

On the structure of some $p$-adic period domains

We study the geometry of the p-adic analogues of the complex analytic period spaces first introduced by Griffiths. More precisely, we prove the Fargues-Rapoport conjecture for p-adic period domains: for a reductive group G over a p-adic field and a minuscule cocharacter µ of G, the weakly admissible locus coincides with the admissible one if and only if the Kottwitz set B(G, µ) is fully Hodge-Newton decomposable.

On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility

Abstract A generalisation of m-expansive Hilbert space operators T ∈ B(ℋ) [18, 20] to Banach space operators T ∈ B(𝒳) is obtained by defining that a pair of operators A, B ∈ B(𝒳) is (m, P)-expansive for some operator P ∈ B(𝒳) if Δ A,B m (P)= ( I - L A R B ) m ( P ) = ∑ j = 0 m ( - 1 ) j ( j m ) {\left( {I - {L_A}{R_B}} \right)^m}\left( P \right) = \sum\nolimits_{j = 0}^m {{{\left( { - 1} \right)}^j}\left( {_j^m} \right)} AjPBj ≤0; LA(X) = AX and RB(X)=XB. Unlike m-isometric and m-left invertible operators, commuting products and perturbations by commuting nilpotents of (m, I)-expansive operators do not result in expansive operators: using elementary algebraic properties of the left and right multiplication operators, a sufficient condition is proved. For Drazin invertible A and B ∈ B(ℋ), with Drazin inverses Ad and Bd, a sufficient condition proving (Ad, Bd) ^ (A, B) is (m − 1, P)-isometric (resp., (m − 1, P)-contractive) for m even (resp., m odd) is given, and a Banach space analogue of this result is proved.

High-Fidelity Optical Transmission Around the Corner

It is a great challenge to use visible and coherent light source to realize high-fidelity optical transmission in free space around the corner where blockade, reflection and scattering occur, and quality of the information retrieved at the receiving end is significantly affected. In this Letter, we propose a novel method to solve the problems encountered in data transmission in free space around the corner when visible and coherent light source is applied. The proposed method is highly robust to coherent light diffraction, multiple scattering effect and environmental noise, which can make it promising for practical applications. A number of optical experiments have been conducted to successfully transmit different types of signals (e.g., analog) in free space around the corner to achieve high fidelity. The proposed method could lead to a development in many relevant applications, e.g., optical transmission in free space, information propagation in free space, telecommunication, and optical security.

Kibble-Zurek Behavior in Disordered Chern Insulators.

Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly nonlocal Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Because of disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the nonequilibrium postquench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.

Team Processes and Outcomes During the AMADEE-18 Mars Analog Mission.

The aim of this study was to examine team functioning within the context of the AMADEE 18 Mars analog project, which took place in Oman in the winter of 2018. Five "Analog Astronauts" participated in this study. Each completed measures of individual-level variables, including demographics and personality, before the simulated Mars mission began. At several time points during the mission, and once at the end, participants completed measures of individual stress reactions, and teamwork-related variables, including several types of team conflict, citizenship behavior, in-role behavior, counterproductive behavior, and social loafing. Each participant also reported how well he or she felt the team performed. The results indicate an overall positive, successful teamwork experience. Factors including measurement issues, psychological simulation fidelity, and qualities of the team likely influenced these results. Measuring important team- and individual-level variables during additional space analog events, while considering factors related to psychological fidelity, will allow for the compilation of data to better understand the factors affecting teams in these unusual contexts.

A story of diameter, radius, and (almost) Helly property

AbstractWe present new algorithmic results for the class of Helly graphs, that is, for the discrete analogues of hyperconvex metric spaces. Specifically, an undirected unweighted graph is Helly if every family of pairwise intersecting balls has a nonempty common intersection. It is known that every graph isometrically embeds into a Helly graph that makes of the latter an important class of graphs in metric graph theory. We study diameter and radius computations within the Helly graphs, and related graph classes. This is in part motivated by a conjecture on the fine‐grained complexity of these two distance problems within the graph classes of bounded fractional Helly number—that contain as particular cases the proper minor‐closed graph classes and the bounded clique‐width graphs. Note that under plausible complexity assumptions, neither the diameter nor the radius can be computed in truly subquadratic time on general graphs. In contrast to these negative results, we first present algorithms which given an n‐vertex m‐edge Helly graph G as input, compute with high probability (w.h.p.) its radius and its diameter in time (i.e., subquadratic in n + m). Our algorithms are based on the Helly property and on the unimodality of the eccentricity function in Helly graphs: every vertex of locally minimum eccentricity is a central vertex. Then, we improve our results for the C4‐free Helly graphs, that are exactly the Helly graphs whose balls are convex. For this subclass, we present linear‐time algorithms for computing the eccentricity of all vertices. Doing so, we generalize previous results on strongly chordal graphs to a much larger subclass, that includes, among others, all the bridged Helly graphs and the hereditary Helly graphs. Lastly, we derive approximate versions of our results for the class of chordal graphs: with the latter satisfying an almost‐Helly‐type property, and a stronger (induced‐path) convexity property than the C4‐free Helly graphs. For the chordal graphs, we can compute in quasi linear time the eccentricity of all vertices with an additive one‐sided error of at most one, which is best possible under the strong exponential‐time hypothesis. This answers an open question of Dragan. In fact, we obtain this last result as a byproduct from a more general reduction: from diameter computation on chordal graphs to the Disjoint Sets problem. Roughly, it implies that the split graphs are the only hard instances for diameter computation on chordal graphs. We also get from our reduction that on any subclass of chordal graphs with constant VC‐dimension (and so, for undirected path graphs), the diameter can be computed in truly subquadratic time.

Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups

We study measures on a real separable Hilbert space that are invariant under translations by arbitrary vectors in . We define the Hilbert space of complex-valued functions on square-integrable with respect to some translation-invariant measure . We determine the expectations of the operators of shift by random vectors whose distributions are given by semigroups (with respect to convolution) of Gaussian measures on . We prove that these expectations form a semigroup of self-adjoint contractions on . We obtain a criterion for the strong continuity of such semigroups and study the properties of their generators (which are self-adjoint generalizations of Laplace operators to the case of functions of infinite-dimensional arguments). We introduce analogues of Sobolev spaces and spaces of smooth functions and obtain conditions for the embedding and dense embedding of spaces of smooth functions in Sobolev spaces. We apply these function spaces to problems of approximating semigroups by the expectations of random processes and study properties of our generalizations of Laplace operators and their fractional powers.

Spherical contours, IR divergences and the geometry of Feynman parameter integrands at one loop

Spherical contours introduced in [1] translate the concept of “discontinuity across a branch cut” to Feynman parameter space. In this paper, we further explore spherical contours and connect them to the computation of leading IR divergences of 1 loop graphs directly in Feynman parameter space. These spherical contours can be used to develop a Feynman parameter space analog of “Leading Singularities” of loop integrands which allows us to develop a method of determining Feynman parameter integrands without the need to sum over Feynman diagrams in momentum space. Finally, we explore some interesting features of Feynman parameter integrands in mathcal{N} = 4 SYM.

Dirichlet Problem for Poisson Equation on the Rectangle in Infinite Dimensional Hilbert Space

Abstract We study the class of finite additive shift invariant measures on the real separable Hilbert space E. For any choice of such a measure we consider the Hilbert space ℋ of complex-valued functions which are square-integrable with respect to this measure. Some analogs of Sobolev spaces of functions on the space E are introduced. The analogue of Gauss theorem is obtained for the simplest domains such as the rectangle in the space E. The correctness of the problem for Poisson equation in the rectangle with homogeneous Dirichlet condition is obtained and the variational approach of the solving of this problem is constructed.

Symmetric Quantum Sets and L-Algebras

Abstract Quantum analogues of sets are defined by two simple assumptions, allowing enumeration, reminiscent of the Gram–Schmidt orthogonalization process. It is shown that any symmetric quantum set is a classical set of irreducible components, and that each irreducible component of size $>3$ is representable by an orthomodular space over a skew field with involution. For finite or sufficiently large irreducible components, invariance of quantum cardinality is proved. Topological quantum sets are introduced as quantum analogues of topological spaces; irreducible ones of size $>3$ are shown to be representable by Hilbert spaces over ${\mathbb{R}}$, ${\mathbb{C}}$, or ${\mathbb{H}}$. Symmetric quantum sets are characterized as a class of $L$-algebras with an intrinsic geometry, and they are shown to be equivalent to Piron’s quantum formalism. Equivalences between symmetric quantum sets and several other structures are established. To any symmetric quantum set, a group with a right invariant lattice structure is associated as a complete invariant. A simple and self-contained proof of Solèr’s theorem is included, which is used to prove that sufficiently large irreducible symmetric quantum sets come from a classical Hilbert space.

An Evaluation Formula for Radon–Nikodym Derivatives Similar to Conditional Expectations over Paths

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition $$0=t_0<t_1<\cdots <t_n=T$$ of [0, T], define $$X:C[0,T]\rightarrow \mathbb R^{n+1}$$ by $$X(x)=(x(t_0),x(t_1),\ldots ,$$ $$x(t_n))$$ . In this paper, we derive a simple evaluation formula for Radon–Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X which has a drift and an initial weight. As applications of the formula, we evaluate the Radon–Nikodym derivatives of the functions $$\int _0^T[x(t)]^m\mathrm{d}\lambda (t)(m\in \mathbb N)$$ and $$[\int _0^Tx(t)\mathrm{d}\lambda (t)]^2$$ on C[0, T], where $$\lambda $$ is a complex-valued Borel measure on [0, T].

Long colimits of topological groups II: Free groups and vector spaces

Topological properties of the free topological group and the free abelian topological group on a space have been thoroughly studied since the 1940s. In this paper, we study the free topological R-vector space V(X) on X. We show that V(X) is a quotient of the free abelian topological group on [−1,1]×X, and use this to prove topological vector space analogues of existing results for free topological groups on pseudocompact spaces. As an application, we show that certain families of subspaces of V(X) satisfy the so-called algebraic colimit property defined in the authors' previous work.

Changes in Sensory Functions in Response to Living in an Extreme Underwater Saturation Environment

The present challenges of long duration spaceflight and other missions in extreme environments include changes of sensory functions, including vision impairment and changes in taste perception. In order to monitor and improve astronaut health and performance during long duration spaceflight and future spaceflight missions we studied sensory functions in response to living in an extreme environment during the NASA Extreme Environment Mission Operation (NEEMO) 23. The Aquarius Reef Base is located at 20 m (66 ft) with 2.6 atm (air) pressure inside the habitat, while levels of CO2 are elevated similarly to the International Space Station.This study assessed the changes in visual acuity and taste perception in 6 NEEMO 23 subjects (2 males, 4 females) 1 day before the mission, during the mission at half time and 1 day post mission. Visual changes were assessed using the NIH Toolbox protocol, while changes in taste perception were measured using solutions containing concentrations of either salty, sweet and bitter flavors in three different concetrations on the side of the tongue and in full mouth.We observed a trend of decreased salty and bitter taste sensation in the habitat and post mission, compared to baseline, while the sweet taste sensation did not change. When testing the full mouth, the salty taste sensation significantly decreased post mission, compared to baseline at low or medium concentration. Bitter taste sensation significantly decreased at low concentration in habitat and post mission, compared to baseline. At medium concentration the bitter taste sensation significantly decreased post mission, compared to baseline and in‐habitat, while at high concentration it significantly decreased post mission, compared to baseline. There was a signifcant reduction in the Overall Raw and in Overall Uncorrected Vision Scores between baseline and post mission indicating a significant reduction in visual acuity during the 9 days mission that was not restored immediately after the mission.Living in a saturation environment decreases certain sensory modalities that may persist for an unknown length of time after the exposure. Diminished sensitivity to taste can alter nutritional status and chemosensory changes may also relate to space sickness, stress and psychological factors, while changes in vision may impair operational tasks. These data indicate that mitigation strategies need to be developed and tested in space analog environments.Support or Funding InformationKetone Technologies LLC provided partial funding for the study. SIFT provided partial salary for CA.

A Reflection on 50 Years of John Maynard Smith's "Protein Space".

In 1970, John Maynard Smith published a letter, entitled "Natural Selection and the Concept of a Protein Space," that proposed a simple analogy for the incremental process of adaptive evolution. His "Protein Space" analogy contains the substrate for many central ideas in evolutionary genetics, and has motivated important discoveries within several subdisciplines of evolutionary science. In this Perspectives article, I commemorate the 50th anniversary of this seminal work by discussing its unique legacy and by describing its intriguing historical context. I propose that the Protein Space analogy is not only important because of its scientific richness, but also because of what it can teach us about the art of constructing useful and subversive analogies.

Пространства Соболева и краевые задачи для операторов ротор и градиент дивергенции

В ограниченной области $G\subset \mathbb{R}^3$ с гладкой границей изучаются краевые и спектральные задачи для операторов $\operatorname{rot} +\lambda I$ и $\nabla \operatorname{div} +\lambda I$ в пространствах Соболева. При $\lambda\neq 0$ операторы расширяются (методом Б. Вайнберга и В. Грушина) до эллиптических матриц, а краевые задачи удовлетворяют условиям эллиптичности В. Солонникова. Из теории и оценок вытекают полезные свойства решений спектральных задач. Операторы $\nabla \operatorname{div}$ и $ \operatorname{rot}$ имеют самосопряженные расширения $\mathcal{N}_d$ и $\mathcal{S}$ в ортогональные подпространства $\mathcal{A}_{\gamma }$ и $V^0$ потенциальных и вихревых полей в $\mathbf{L}_{2}(G)$, а их собственные векторы задают ортогональные базисы в $\mathcal{A}_{\gamma }$ и $V^0$, элементы которых представляются рядами Фурье, а операторы - преобразованиями рядов. Определены аналоги пространств Соболева $\mathbf{A}^{2k}_{\gamma }$ и $\mathbf{W}^m$ порядков $2k$ и $m$ в классах потенциальных и вихревых полей и классы $ C(2k,m)$ их прямых сумм. Доказано, что при $\lambda\neq \operatorname{Sp}(\operatorname{rot})$ оператор $ \operatorname{rot}+\lambda I$ отображает класс $C(2k,m+1)$ на класс $C(2k,m)$ взаимно однозначно и непрерывно, а при $\lambda\neq \operatorname{Sp}(\nabla \operatorname{div})$ оператор $\nabla \operatorname{div}+\lambda I$ отображает $C(2(k+1), m)$ на $C(2k,m)$ соответственно.

Irreversible energy transfer, localization and non-reciprocity in weakly coupled, nonlinear lattices with asymmetry

A semi-infinite network of two coupled semi-infinite nonlinear lattices is studied, having the capacity for passive irreversible energy transfer (redirection) from an “excited lattice” (forced by an impulse) to an “absorbing lattice” (that is not directly forced). This is achieved by breaking the symmetry through a spatial variation of the grounding stiffnesses of the excited lattice from the second unit cell onwards, and assuming weak coupling. We show analytically that irreversible energy transfer is caused by the macroscopic analogue (in space) of the Landau–Zener tunneling (LZT) effect, which originated in quantum mechanics in the context of linear parametric oscillators (in time). By constructing a reduced-order model (ROM) of two coupled oscillators it is possible to theoretically model the LZT-induced irreversible energy redirection from the excited to the absorbing lattice. A computational study reveals that the LZT effect is realized only in a critical band of energy, while outside this band there occurs energy localization. The lower and upper energy bounds of this critical band are theoretically approximated by constructing appropriate ROMs of the coupled lattices and studying the bifurcations in their dynamics with energy. This analysis sheds physical insight on the different regimes of the acoustics, and theoretical predictions agree well with direct numerical simulations of the full lattice network. Finally, we show that the LZT effect induces strong non-reciprocity in the dynamics of the finite asymmetric lattice network, in the sense that the impulsive response of this network depends crucially on the forcing-measurement locations and energy. The implications and the possible applications of these results are discussed.

Clark measures on the complex sphere

Let Bd denote the unit ball of Cd, d≥1. Given a holomorphic function φ:Bd→B1, we study the corresponding family σα[φ], α∈∂B1, of Clark measures on the unit sphere ∂Bd. If φ is an inner function, then we introduce and investigate related unitary operators Uα mapping analogs of model spaces onto L2(σα), α∈∂B1. In particular, we explicitly characterize the set of Uα⁎f such that fσα is a pluriharmonic measure. Also, for an arbitrary holomorphic φ:Bd→B1, we use the family σα[φ] to compute the essential norm of the composition operator Cφ:H2(B1)→H2(Bd).