Even before the Covid-19 pandemic, beneficial use cases for hygienic, touchless human-machine interaction have been explored. Gaze input, i.e., information input via eye-movements of users, represents a promising method for contact-free interaction in human-machine systems. In this paper, we present the GazeVending interface (GaVe), which lets users control actions on a display with their eyes. The interface works on a regular webcam, available on most of today's laptops, and only requires a one-point calibration before use. GaVe is designed in a hierarchical structure, presenting broad item cluster to users first and subsequently guiding them through another selection round, which allows the presentation of a large number of items. Cluster/item selection in GaVe is based on the dwell time of fixations, i.e., the time duration that users look at a given Cluster/item. A user study (N=22) was conducted to test optimal dwell time thresholds and comfortable human-to-display distances. Users' perception of the system, as well as error rates and task completion time were registered. We found that all participants were able to use the system with a short time training, and showed good per
How quasars powered by supermassive black holes (SMBHs) formed less than a billion years after the Big Bang is still one of the outstanding problems in astrophysics 20 years after their discovery$^{1-4}$. Cosmological simulations suggest that rare cold flows converging on primordial haloes in low-shear environments could have created these quasars if they were 10$^4$ - 10$^5$ M$_{\odot}$ at birth but could not resolve their formation$^{5-8}$. Semianalytical studies of the progenitor halo of a primordial quasar found that it favours the formation of such seeds but could not verify if one actually appeared$^9$. Here we show that a halo at the rare convergence of strong, cold accretion flows creates massive BH seeds without the need for UV backgrounds, supersonic streaming motions, or even atomic cooling. Cold flows drive violent, supersonic turbulence in the halo that prevents star formation until it reaches a mass that triggers sudden, catastrophic baryon collapse that forms 31,000 and 40,000 M$_{\odot}$ stars. This simple, robust process ensures that haloes capable of forming quasars by z $>$ 6 produce massive seeds. The first quasars were thus a natural consequence of structure
As part of the Herschel Guaranteed Time Key Programme CHESS, we present the discovery of a diffuse gas component in the foreground of the intermediate-mass protostar OMC-2 FIR 4, located in the Orion A region. Making use of the full HIFI spectrum of OMC-2 FIR 4 obtained in CHESS, we detected several ground-state lines from OH+, H2O+, HF, and CH+, all of them seen in absorption against the dust continuum emission of the protostar's envelope. The lines peak at a velocity of 9 km/s, which is blue-shifted by 2 km/s with respect to the systemic velocity of OMC-2 FIR 4 (V = 11.4 km/s). We derived column densities for each species, as well as an upper limit to the column density of the undetected H3O+. In order to model and characterise the foreground cloud, we used the Meudon PDR code to run a homogeneous grid of models that spans a reasonable range of densities, visual extinctions, cosmic ray ionisation rates and far-ultraviolet (FUV) radiation fields. The results of our modelling indicate that the foreground cloud is composed of predominantly neutral diffuse gas (n(H) = 100 cm-3) and is heavily irradiated by an external source of FUV that most likely arises from the nearby Trapezium OB
The 30 Doradus Nebula in the Large Magellanic Cloud (LMC) contains the massive starburst cluster NGC 2070 with a massive and probably younger stellar sub clump at its center: R136. It is not clear how such a massive inner cluster could form several million years after the older stars in NGC 2070, given that stellar feedback is usually thought to expel gas and inhibit further star formation. Using the recently developed 1D feedback scheme WARPFIELD to scan a large range of cloud and cluster properties, we show that an age offset of several million years between the stellar populations is in fact to be expected given the interplay between feedback and gravity in a giant molecular cloud (GMC) with a density $\gtrsim 500$ cm$^{-3}$ due to re-accretion of gas onto the older stellar population. Neither capture of field stars nor gas retention inside the cluster have to be invoked in order to explain the observed age offset in NGC 2070 as well as the structure of the interstellar medium (ISM) around it.
Cauchy's contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Bjorling, an infinitesimal definition of the criterion of uniform convergence. Cauchy's foundational stance is hereby reconsidered.
Y. Miyashita gave characterizations of a separable polynomial and a Hirata separable polynomial in skew polynomial rings. In the previous paper, the author and S. Ikehata gave direct and elementary proofs of Miyashita's theorems in skew polynomial rings of automorphism type $B[X;ρ]$ and derivation type $B[X;D]$, respectively. The purpose of this paper is to give proofs for them in the general skew polynomial ring $B[X;ρ,D]$.
Let $G$ be a real reductive Lie group and $H$ a reductive subgroup of $G$. Benoist-Kobayashi studied when $L^2(G/H)$ is a tempered representation of $G$. They introduced the functions $ρ$ on Lie algebras and gave a necessary and sufficient condition for the temperedness of $L^2(G/H)$ in terms of an inequality on $ρ$. In a joint work with Y. Oshima, we considered when $L^2(G/H)$ is equivalent to a unitary subrepresentation of $L^2(G)$ and gave a sufficient condition for this in terms of a strict inequality of $ρ$. In this paper, we will classify the pairs $(\mathfrak{g}, \mathfrak{h})$ with $\mathfrak{g}$ complex reductive and $\mathfrak{h}$ complex semisimple which satisfy that strict inequality of $ρ$.
An underdetermined generalized absolute value equation (GAVE) may have no solution, one solution, finitely many or infinitely many solutions. This paper is concerned with sufficient conditions that guarantee the existence of solutions to an underdetermined GAVE. Particularly, sufficient conditions are established for an underdetermined GAVE to have infinitely many solutions with no zero entry that possess a particular or any given sign pattern. Iterative methods are proposed for the case when the underdetermined GAVE does have a solution. Some existing results for square GAVE are also extended.
In 1974, Erdős asked the following question: given a graph $G$ and a directed graph $\vec{H}$, how many ways are there to orient the edges of $G$ such that it does not contain $\vec{H}$ as a subgraph? We denote this value by $D(G, \vec{H})$. Further, we let $D(n, \vec{H})$ denote the maximum of $D(G, \vec{H})$ over all graphs $G$ on $n$ vertices. In 2006, Alon and Yuster gave an exact answer when $\vec{H}$ is a tournament. In 2023, Bucić, Janzer, and Sudakov gave asymptotic answers for all directed graphs $\vec{H}$, and in the same paper, they gave an exact answer when $\vec{H}$ is a directed cycle. In this paper, we give a better bound for some specific non-bipartite directed graphs. Further, we obtain exact values of $D(G, \vec{H})$ for some small non-edge-critical directed graphs $\vec{H}$. Finally, for these graphs, we classify all graphs $G$ that attain the bound $D(G, \vec{H}) = D(n, \vec{H})$.
Randomized iterative methods, such as the Kaczmarz method and its variants, have gained growing attention due to their simplicity and efficiency in solving large-scale linear systems. Meanwhile, absolute value equations (AVE) have attracted increasing interest due to their connection with the linear complementarity problem. In this paper, we investigate the application of randomized iterative methods to generalized AVE (GAVE). Our approach differs from most existing works in that we tackle GAVE with non-square coefficient matrices. We establish more comprehensive sufficient and necessary conditions for characterizing the solvability of GAVE and propose precise error bound conditions. Furthermore, we introduce a flexible and efficient randomized iterative algorithmic framework for solving GAVE, which employs randomized sketching matrices drawn from user-specified distributions. This framework is capable of encompassing many well-known methods, including the Picard iteration method and the randomized Kaczmarz method. Leveraging our findings on solvability and error bounds, we establish both almost sure convergence and linear convergence rates for this versatile algorithmic framework.
The Traveling Salesman Problem (TSP) in the $d$-dimensional Euclidean space is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial time approximation schemes. To improve the running time, Rao and Smith [STOC 1998] gave a randomized $(1/\varepsilon)^{O(1/\varepsilon^{d-1})}\cdot n\log n$ time approximation scheme. Bartal and Gottlieb [FOCS 2013] gave a randomized approximation scheme in $2^{(1/\varepsilon)^{O(d)}} n$ time, which is linear in $n$. Recently, Kisfaludi-Bak, Nederlof, and Węgrzycki [FOCS 2021] gave a randomized approximation scheme in $2^{O(1/\varepsilon^{d-1})} n \log n$ time, achieving a Gap-ETH tight dependence on $\varepsilon$. It is raised as a challenging open question by Kisfaludi-Bak, Nederlof, and Węgrzycki [FOCS 2021] whether a running time of $2^{O(1/\varepsilon^{d-1})}n$ is achievable. We answer their question positively by giving a randomized $2^{O(1/\varepsilon^{d-1})} n$ time approximation scheme for Euclidean TSP.
Sandqvist gave a proof-theoretic semantics (P-tS) for classical logic (CL) that explicates the meaning of the connectives without assuming bivalance. Later, he gave a semantics for intuitionistic propositional logic (IPL). While soundness in both cases is proved through standard techniques, the proof completeness for CL is complex and somewhat obscure, but clear and simple for IPL. Makinson gave a simplified proof of completeness for classical propositional logic (CPL) by directly relating the the P-tS to the logic's extant truth-functional semantics. In this paper, we give an elementary, constructive, and native -- in the sense that it does not presuppose the model-theoretic interpretation of classical logic -- proof of completeness the P-tS of CL using the techniques applies for IPL. Simultaneously, we give a proof of soundness and completeness for first-order intuitionistic logic (IL).
In an earlier book of Arthur, the endoscopic classification of representations of quasi-split orthogonal and symplectic groups was established. Later Mok gave that of quasi-split unitary groups. After that, Kaletha, Minguez, Shin, and White gave that of non-quasi-split unitary groups for generic parameters. In this paper we prove the endoscopic classification of representations of non-quasi-split odd special orthogonal groups for generic parameters, following Kaletha, Minguez, Shin, and White.
Cantor gave in his fundamental article an elegant proof of the countability of real algebraic numbers based on a positive integer height, denoted by him as N, of integer and irreducible polynomials of given degree (denoted by him as n) with relative prime coefficients. The finite number of real algebraic numbers with given height he called phi(N), and gave the first three instances.\pn Here we give a systematic list for the real algebraic numbers of height, which we denote by n, for n from 1 to 7 and polynomials of degree k.
We show that a simple single-pass semi-streaming variant of the Pivot algorithm for Correlation Clustering gives a (3 + ε)-approximation using O(n/ε) words of memory. This is a slight improvement over the recent results of Cambus, Kuhn, Lindy, Pai, and Uitto, who gave a (3 + ε)-approximation using O(n log n) words of memory, and Behnezhad, Charikar, Ma, and Tan, who gave a 5-approximation using O(n) words of memory. One of the main contributions of this paper is that both the algorithm and its analysis are very simple, and also the algorithm is easy to implement.
An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.
In 2016 Izadi and Nabardi (b) showed (4-2-4) has infinitely many integer solutions. They used a specific congruent number elliptic curve.In 2019 Janfada and Nabardi,item C, showed that a necessary condition for n to have an integral solution for the above equation and gave a parametric solution.They gave the numeric solutions for n=41,136,313,1028,1201,3281. In 2020 Ajai Choudhry , Iliya Bluskov and Alexander James (a), showed that equation (4-2-4) has infinitely many parametric solutions. They gave the numeric solutions for n=17,257,626,641,706,1921.
Bernstein fits implemented into R allow another route for Kruskal-Wallis power-study tool development. Monte-Carlo Kruskal-Wallis power studies were compared with measured power, with Monte-Carlo ANOVA equivalent and with an analytical method, with or without normalization, using four simulated runs each with 60-100 populations (each population with N=30000 from a set of Pearson-type ranges): random selection gave 6300 samples analysed for predictive power. Three medical-study datasets (Dialysis/systolic blood pressure; Diabetes/sleep-hours; Marital-status/high-density-lipoprotein cholesterol) were also analysed. In three from four simulated runs (run_one, run_one_relaxed, and run_three) with Pearson types pooled, Monte-Carlo Kruskal-Wallis gave predicted sample sizes significantly slightly lower than measured but more accurate than with ANOVA methods; the latter gave high sample-size predictions. Populations (run_one_relaxed) with ANOVA assumptions invalid gave Kruskal-Wallis predictions similar to those measured. In two from three medical studies, Kruskal-Wallis predictions (Dialysis: similar predictions; Marital: higher than measured) were more accurate than ANOVA (both higher t
Wolf gave a homeomorphism from the Teichmüller space to the space of quadratic differentials on a closed Riemann surface by using harmonic maps. Moreover, using harmonic maps rays, he gave a compactification of the Teichmüller space and show that it coincides with the Thurston compactification. In this paper, we extend the harmonic maps compactification to the Teichmüller spaces of punctured Riemann surfaces, and show that it still coincides with the Thurston compactification.