Miracle-dz/UniFAR-FTUs huggingface dataset:
A fermionic de Finetti theorem

Quantum versions of de Finetti’s theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles fo.
Optimal control on graphs: existence, uniqueness, and long-term behavior

The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with results on the associated ergodic Hamilton-Jacobi equation.
Global well-posedness of the Benjamin-Ono equation in H^1(R)

We show that the Benjamin-Ono equation is globally well-posed in $H^s(\R)$ for $s \geq 1$. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be uniformly continuous in $H^s$ for any $s$. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.
Low level representations for E(10) and E(11)

We work out the decomposition of the indefinite Kac Moody algebras E10 and E11 w.r. t. their respective subalgebras A9 and A10 at low levels. Tables of the irreducible representations with their outer multiplicities are presented for E10 up to level ell = 18 and for E11 up to level ell =10. On the way we confirm and extend existing results for E10 root multiplicities, and for the first time compute non-trivial root multiplicities of E11.
Groups acting on hyperbolic $\Lambda$-metric spaces

In this paper we study group actions on hyperbolic $\Lambda$-metric spaces, where $\Lambda$ is an ordered abelian group. $\Lambda$-metric spaces were first introduced by Morgan and Shalen in their study of hyperbolic structures and then Chiswell, following Gromov's ideas, introduced the notion of hyperbolicty for such spaces. Only the case of 0-hyperbolic $\Lambda$-metric spaces (that is, $\Lambda$-trees) was systematically studied, while the theory of general hyperbolic $\Lambda$-metric spaces was not developed at all. Hence, one of the goals of the present paper was to fill this gap and translate basic notions and results from the theory of group actions on hyperbolic (in the usual sense) spaces to the case of $\Lambda$-metric spaces for an arbitrary $\Lambda$. The other goal was to show some principal difficulties which arise in this generalization and the ways to deal with them.
Homotopy theory of complete Lie algebras and Lie models of simplicial sets

In a previous work, by extending the classical Quillen construction to the non‐simply connected case, we have built a pair of adjoint functors, model and realization, between the categories of simplicial sets and complete differential graded Lie algebras. This paper is a follow‐up of this work. We show that when X is a finite connected simplicial set, then ⟨LX⟩ coincides with Q∞X+ , the disjoint union of the Bousfield–Kan completion of X with an external point. We also define a model category structure on cDGL making L and ⟨−⟩ a Quillen pair, and we construct an explicit cylinder. In particular, these functors preserve homotopies and weak equivalences and therefore, this gives the basis for developing a cDGL rational homotopy theory for all spaces.
Comparative Study of Foot Fixation Methods and Sensor Arrangements in Ankle Joint Torque Measurement Equipment

Joint torque estimation techniques are used for evaluating human motor function. Particularly, ankle joint torque is essential for evaluating the walking function. Ankle joint torque can be derived by fixing the metatarsophalangeal (MTP) joint and ankle circumference and measuring force and torque from force sensors placed at the two fixation points. Considering implementation effort, it is desirable to use a 6-axis sensor or a sensor with fewer measurable axes. Therefore, in this study, we compared multiple sensor arrangements and calculation methods in the measurement of ankle joint torque. Through theoretical and empirical evaluations, the conditions under which these methods are effective were clarified. Based on the investigation, we propose a method to arrange a 6-axis force sensor only at the toe. One concern in the theoretical investigation was the error due to the moment caused by the fixation of the heel side. However, in measurement experiments using an ankle model and subjects, the accuracy was almost the same as when two 6-axis force sensors were used. The results indicates that the effect of this error factor is limited: hence, this method is considered to be useful as a method of both accuracy and sensor reduction.
A representation theorem on a filtering model with first-passage-type stopping time

We present a representation theorem for a filtering model with first-passage-type stopping time. The model is constructed from two unobservable processes and one observable process that is under the influence of two unobservable processes.A filter is constructed using Brownian motion in the observable process and a first-passage-type stopping time in an unobservable process.Though our theorems are similar to those of Nakagawa\cite{Nakagawa}, we do not use pinned Brownian motion measure, which is difficult to deal with. In addition, we describe a representation theorem for another filtration that was not discussed by Nakagawa
Nowhere-zero $3$-flow and $\mathbb{Z}_3$-connectedness in Graphs with Four Edge-disjoint Spanning Trees

Given a zero-sum function $\beta : V(G) \rightarrow \mathbb{Z}_3$ with $\sum_{v\in V(G)}\beta(v)=0$, an orientation $D$ of $G$ with $d^+_D(v)-d^-_D(v)= \beta(v)$ in $\mathbb{Z}_3$ for every vertex $v\in V(G)$ is called a $\beta$-orientation. A graph $G$ is $\mathbb{Z}_3$-connected if $G$ admits a $\beta$- orientation for every zero-sum function $\beta$. Jaeger et al. conjectured that every $5$-edge-connected graph is $\mathbb{Z}_3$-connected. A graph is $\langle\mathbb{Z}_3\rangle$-extendable at vertex $v$ if any pre-orientation at $v$ can be extended to a $\beta$-orientation of $G$ for any zero-sum function $\beta$. We observe that if every $5$-edge-connected essentially $6$-edge-connected graph is $\langle\mathbb{Z}_3\rangle$-extendable at any degree five vertex, then the above mentioned conjecture by Jaeger et al. holds as well. Furthermore, applying the partial flow extension method of Thomassen and of Lov\'{a}sz et al., we prove that every graph with at least 4 edge-disjoint spanning trees is $\mathbb{Z}_3$-connected. Consequently, every $5$-edge-connected essentially $23$-edge-connected graph is $\langle\mathbb{Z}_3\rangle$-extendable at degree five vertex.
Cardiovascular health status in Chinese Cardiologists: China Cardiologist Heart Survey II

Background and purpose: Cardiologists represent a subset of the population with the highest degree of awareness to cardiovascular diseases (CVD), and thus should have low exposure to modifiable risks and low CVD prevalence. However, the status of cardiovascular health in Chinese cardiologists remains unknown. Methods: China Cardiologist Heart Survey II is a nation-wide cross-sectional survey on licensed cardiologists in Chinese mainland. It was conducted between August 2020 and November 2021. An online questionnaire was used to acquire demographic and lifestyle information, cardiovascular risk factors, CVD status, and medications. Crude prevalence of cardiovascular risk factors, organ damage, and CVD were calculated and compared between sexes and between sub-specialties. Age-weighted prevalence of cardiovascular risk factors were compared to that in the general Chinese population in the literature. Results: The final analysis included a total of 15,827 cardiologists at the age of 25 to 60 years from 31 provinces. The median age was 38 years and 8650 (54.7%) were men. The most common cardiovascular risk factor was family history of premature CVD (20.4%), followed by hypertension (12.4%), hyperlipidemia (10.6%), overweight/obesity (8.3%), smoking (7.3%), and diabetes (2.4%). The most common sub-clinical organ damages included carotid plaque (3.4%) and microalbuminuria (1.2%). The rate of confirmed coronary artery disease was 0.4%. The rate of arrhythmia was 3.1%. The rate of obstructive sleep apnea syndrome was 2.2%. The rate of cardiovascular risk factors and organ damage was higher in men versus in women, and higher in interventional versus non-interventional cardiologists. In comparison to the data reported for the general population in China, cardiologists had lower age-weighted prevalence of hypertension (15.2% vs. 23.2%), diabetes (3.1% vs. 10.9%), hyperlipidemia (12.3% vs. 40.4%), obesity (2.1% vs. 11.9%), and smoking (7.7% vs. 27.7%). Conclusions: In comparison to the general public, cardiologists in Chinese mainland had much lower age-weighted prevalence of cardiovascular risk factors, but there is substantial room for further improvement, particularly in male and interventional cardiologists.
Conic James' Compactness Theorem

Our main result is the following: {\it Let $E$ be a Banach space and $D$ be a weakly compact subset of $E$ with $0\notin D$. If $A$ is a bounded subset of $E$ such that every $x^*\in E^*$ with $x^*(D) >0$ attains its supremum on $A$, then $A$ is weakly relatively compact. }
Motion-Driven Spatial and Temporal Adaptive High-Resolution Graph Convolutional Networks for Skeleton-Based Action Recognition

Graph convolutional networks (GCN) have attracted increasing interest in action recognition in recent years. GCN models human skeleton sequences as spatio-temporal graphs. Also, attention mechanisms are often jointly used with GCNs to highlight important frames or body joints in a sequence. However, attention modules learn parameters offline and are fixed, so may not adapt well to unseen samples. In this paper, we propose a simple but effective motion-driven spatial and temporal adaptation strategy to dynamically strengthen the features of important frames and joints for skeleton-based action recognition. The rationale is that the joints and frames with dramatic motions are generally more informative and discriminative. We combine the spatial and temporal refinements by using a two-branch structure, in which the joint and frame-wise feature refinements perform in parallel. Such a structure can lead to learn more complementary feature representations. Moreover, we propose to use the fully connected graph convolution to learn the long-range spatial dependencies. Besides, we investigate two high-resolution skeleton graphs by creating virtual joints, aiming to improve the representation of skeleton features. By combining the above proposals, we develop a novel motion-driven spatial and temporal adaptive high-resolution GCN. Experimental results demonstrate that the proposed model achieves state-of-the-art (SOTA) results on the challenging large-scale Kinetics-Skeleton and UAV-Human datasets, and it is on par with the SOTA methods on the two NTU-RGB+D 60&120 datasets. Additionally, our motion-driven adaptation method shows encouraging performance when compared with the attention mechanisms.
A Decomposition Method for Both Additively and Nonadditively Separable Problems

Problem decomposition is crucial for coping with large-scale global optimization problems, which relies heavily on highly precise variable grouping methods. The state-of-the-art decomposition methods identify separability based on the finite differences principle, which is valid only for additively separable functions but not applicable to nonadditively separable functions. Therefore, we need to investigate separability in more depth in order to propose a more general principle and design more universal decomposition methods. In this article, we conduct a comprehensive theoretical investigation on separability, the core of which is proposing an innovative separability identification principle: the minimum points shift principle. By utilizing the new principle, we develop a general separability grouping (GSG) method that can handle both additively and nonadditively separable functions with high accuracy. In addition, we design a new set of benchmark functions based on nonadditive separability, which compensates for the lack of nonadditively separable functions in the previous test suites. Extensive experiments demonstrate that the proposed GSG achieves high grouping accuracy on both new and CEC series benchmark problems, especially on nonadditively separable problems Finally, we verify that the proposed GSG can effectively improve the optimization performance of nonadditively separable problems through optimization experiments.
Intertwining operator for AG2 Calogero–Moser–Sutherland system

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find an intertwining operator between $H$ and the Calogero-Moser-Sutherland Hamiltonian for the root system $G_2$. This gives a quantum integral for $H$ of order 6 in an explicit form thus establishing integrability of $H$.
Universal scaling of current fluctuations in disordered graphene

We analyze the full transport statistics of graphene with smooth disorder at low dopings. First we consider the case of 1D disorder for which the transmission probability distribution is given analytically in terms of the graphene-specific mean free path. All current cumulants are shown to scale with system parameters (doping, size, disorder strength and correlation length) in an identical fashion for large enough systems. In the case of 2D disorder, numerical evidence is given for the same kind of identical scaling of all current cumulants, so that the ratio of any two such cumulants is universal. Specific universal values are given for the Fano factor, which is smaller than the pseudodiffusive value of ballistic graphene (F=1/3) both for 1D (F=0.243) and 2D (F=0.295) disorder. On the other hand, conductivity in wide samples is shown to grow without saturation as \sqrt{L} and Log L with system length L in the 1D and 2D cases respectively.
Detection of Surface Defects in Solar Cells by Bidirectional-Path Feature Pyramid Group-Wise Attention Detector

Due to the multiscale characteristics of defects and strong background interference, the automation of solar cell surface defect detection is still a challenge. To address this problem, this article proposes a novel defect object detector called bidirectional-path group-wise attention detector (BPGA-Detector) which consists of two parts: the bidirectional-path feature pyramid network (BPFPN) and the group-wise attention module (GAM). The BPFPN combines multiscale features using a bidirectional-path feature fusion method that structured by connecting the bottom-up path feature pyramid network (FPN) to the original FPN, preserving the characteristics of minor and weak flaws in the shallow layer. Furthermore, the GAM is elaborately designed to suppress the background disturbance and highlight the defect locations by connecting multilayer contextual features, which significantly improves the discriminant ability of small defects. Finally, the experimental results on a largescale solar cell dataset including 6263 images, 5763 of which are defective, demonstrate that the proposed method achieve superior detection performance (mAP50 up to 88.8%).
Symplectic homology and the Eilenberg-Steenrod axioms

We give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg-Steenrod axioms except for the dimension axiom. The resulting long exact sequence of a pair generalizes various earlier long exact sequences such as the handle attaching sequence, the Legendrian duality sequence, and the exact sequence relating symplectic homology and Rabinowitz Floer homology. New consequences of this framework include a Mayer-Vietoris exact sequence for symplectic homology, invariance of Rabinowitz Floer homology under subcritical handle attachment, and a new product on Rabinowitz Floer homology unifying the pair-of-pants product on symplectic homology with a secondary coproduct on positive symplectic homology. In the appendix, joint with Peter Albers, we discuss obstructions to the existence of certain Liouville cobordisms.
An Intraday Market Design for Colombia’s Energy Transition

The massive promotion of intermittent renewable resources as a decarbonization strategy for economies has led to the need to reconsider current market designs in order to facilitate the integration of this kind of production technology. The intraday market has established itself as an efficient mechanism for these purposes, as has been seen in diverse international experiences, principally Europe. The Colombian electricity market is no stranger to the needs of these reforms, as the National Energy and Mining Planning Office of Colombia (UPME in Spanish) estimates that by 2034 almost 30% of the electricity generation matrix will be comprised of intermittent renewable resources. This paper develops several elements to be considered for the implementation of an intraday market in Colombia, backed with quantitative information, contrary to previous studies that have based their recommendations on qualitative elements. The number of discrete intraday sessions, the effect of changing from a sequential energy and reserve allocation scheme to a co-optimized one, as well as the adjustment mechanism – or a balance mechanism – after the gate closure are, among other aspects, analyzed in this study. The computational simulations executed with real data from two operating months with different characteristics in terms of prices, unavailable assets – a liquidity factor for the new market – and system contingencies support the design elements developed in this study. That is, the proposed design – four sections, co-optimization of energy and reserve, and an adjustment mechanism that is not based only on the use of reserves – tested with real data confirm that this proposal is more convenient than the other kind of design from an operating cost and unavailability management perspective. The results reveal market design elements that must be considered in Colombia and serve as input for other countries – particularly Latin American countries – that are in the process of updating their electricity market designs as part of the current energy transition.
Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries

The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$ a three parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged center of the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a three-dimensional complex hypersurface which remains invariant under the action of an infinite-dimensional group of analytic transformations, called the quantum coadjoint action.
Two-Dimensional Beam Steering Using a Stacked Modulated Geodesic Luneburg Lens Array Antenna for 5G and Beyond

Antennas for future communication systems are required to be highly directive and steerable to compensate for the high path loss in the millimeter-wave band. In this work, we propose a linear array of modulated geodesic Luneburg lens (the so-called water drop lens) antennas operating at 56–62 GHz. The lens array antenna features 2-D beam scanning with low structural complexity. The lenses are fully metallic and implemented in parallel plate waveguides (PPWs), meaning that they are highly efficient. Each lens is fed with 13 rectangular waveguides surrounded by glide-symmetric holes to suppress leakage. The lenses provide <inline-formula> <tex-math notation="LaTeX">$\mathrm{110}^{\circ} $ </tex-math></inline-formula> beam coverage in the H-plane with scan losses below 1 dB. In order to scan in the E-plane, we use a feeding network based on a 1:4 power divider and three phase shifters. In this configuration, the array can scan <inline-formula> <tex-math notation="LaTeX">$\mathrm{60}^{\circ} $ </tex-math></inline-formula> in the E-plane, albeit with higher scanning losses than in the H-plane. The lens array is manufactured and a good agreement between simulated and experimental results is obtained.
Canonical forms for free {\kappa}-semigroups

The implicit signature k consists of the multiplication and the ({\omega}-1)-power. We describe a procedure to transform each {\kappa}-term over a finite alphabet A into a certain canonical form and show that different canonical forms have different interpretations over some finite semigroup. The procedure of construction of the canonical forms, which is inspired in McCammond's normal form algorithm for {\omega}-terms interpreted over the pseudovariety A of all finite aperiodic semigroups, consists in applying elementary changes determined by an elementary set {\Sigma} of pseudoidentities. As an application, we deduce that the variety of {\kappa}-semigroups generated by the pseudovariety S of all finite semigroups is defined by the set {\Sigma} and that the free {\kappa}-semigroup generated by the alphabet A in that variety has decidable word problem. Furthermore, we show that each {\omega}-term has a unique {\omega}-term in canonical form with the same value over A. In particular, the canonical forms provide new, simpler, representatives for {\omega}-terms interpreted over that pseudovariety.