Abstract Funding Acknowledgements Type of funding sources: None. Introduction Atrial fibrillation (AF) is the most common cardiac arrhythmia with an estimated lifetime risk of one in four. Multiple smartwatches capable to "screen" AF are presently available. The sensitivity and specificity for the detection of AF may differ between the available smartwatches, but this has not yet been adequately investigated. Methods We enrolled patients presenting to a cardiology service at a tertiary referral center in a prospective, observational study. The aim of this study was to assess and compare the accuracy of five smartwatches (Apple Watch 6, AliveCor Kardia Mobile, Fitbit Sense, Samsung Galaxy Watch 3 and Withings Scanwatch) in identifying AF compared to a nearly simultaneously acquired physician-interpreted 12-lead ECG in a real world cohort of patients. Each patient was assessed with at least 4/5 smartwatches. Secondary objective was to assess patient preference using smartwatches via predefined questionnaire. Results We prospectively enrolled 163 patients (32.9% female, mean age 64.7 years). AF was present in 47 patients (30.3%) at time of recording. We included 155 patients with 4 or 5 individual recordings for further analysis. Sensitivity and specificity for the detection of AF was similar between smartwatches: 90% and 95% for the Apple Watch 6, 97% and 96% for the AliveCor Kardia Mobile, 86% and 100% for the Fitbit Sense, 97% and 91% for the Samsung Galaxy Watch 3 and 91% and 95% for the Withings Scanwatch, respectively (Figure1). The rate of inconclusive tracings, meaning the algorithm was not able to determine the heart rhythm, was 17%, 26%, 21%, 20% and 24% for the Apple Watch 6, AliveCor Kardia Mobile, Fitbit Sense, Samsung Galaxy Watch 3 and Withings Scanwatch, respectively. Among inconclusive individual tracings from all devices, 63 tracings (40%) were due to high or low heart rate and 50 tracings (31%) due to motion artifacts. The inconclusive recordings were interpreted by blinded cardiologists to determine if these tracings are still clinically useful. By manual review the rhythm could be determined in 98.8% of 741 total individual recorded single-lead ECGs. Regarding patient acceptance, the Apple Watch was ranked first (37%) and the AliveCor Kardia Mobile last (7.6%) when patients were asked about their preferred device for daily rhythm monitoring. Conclusion In this clinical validation of five direct-to-consumer smartwatches we found a high diagnostic accuracy among all assessed smartwatches. We found differences in the amount of inconclusive tracings. In a clinical setting manual review of tracings is required in about one fourth of cases for all assessed smartwatches. In addition, patient’s perception differed between smartwatches. This clinical validation study of these smartwatches may help to better advice patients and physicians in the usage and validity of single-lead ECG-devices for everyday use.
For a language $L$, we consider its cyclic closure, and more generally the language $C^{k}(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators $C^k$. This both sharpens and generalises Brandstädt's result that if $L$ is context-free then $C^{k}(L)$ is context-sensitive and not context-free in general for $k \geq 3$. We also show that the cyclic closure of an indexed language is indexed.
For a connected graph G of order |V(G)| ≥3 and a k-labelling c : E(G) →{1,2,…,k} of the edges of G, the code of a vertex v of G is the ordered k-tuple (ℓ1,ℓ2,…,ℓk), where ℓi is the number of edges incident with v that are labelled i. The k-labelling c is detectable if every two adjacent vertices of G have distinct codes. The minimum positive integer k for which G has a detectable k-labelling is the detection number det(G) of G. In this paper, we show that it is NP-complete to decide if the detection number of a cubic graph is 2. We also show that the detection number of every bipartite graph of minimum degree at least 3 is at most 2. Finally, we give some sufficient condition for a cubic graph to have detection number 3.
We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1. Our main result is to show that for a given g, this conjecture is equivalent to the corresponding case (k = 2g) of a conjecture of Seymour claiming that every planar k-regular multigraph with no odd edge-cut of less than k edges is k-edge-colorable. To this end, we exhibit several properties of signed projective cubes and establish a folding lemma for planar even signed graphs.
Dominique Bontemps, Stephane Boucheron, Elisabeth Gassiat
This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the collection of such classes. The analysis builds on the tight characterization of universal redundancy rate in terms of metric entropy by Haussler and Opper (1997) and on a careful analysis of the performance of the AC-coding algorithm. The latter relies on non-asymptotic bounds for maxima of samples from discrete distributions with finite and non-decreasing hazard rate.
We prove that the Lam-Shimozono ``down operator'' on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of ``near rectangles'' in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of the corresponding k-Littlewood–Richardson coefficients.
We give a polyomino characterisation of recurrent configurations of the sandpile model on the complete bipartite graph $K_{m,n}$ in which one designated vertex is the sink. We present a bijection from these recurrent configurations to decorated parallelogram polyominoes whose bounding box is a $m×n$ rectangle. Other combinatorial structures appear in special cases of this correspondence: for example bicomposition matrices (a matrix analogue of set partitions), and (2+2)-free posets. A canonical toppling process for recurrent configurations gives rise to a path within the associated parallelogram polyominoes. We define a collection of polynomials that we call $q,t$-Narayana polynomials, the generating functions of the bistatistic $(\mathsf{area ,parabounce} )$ on the set of parallelogram polyominoes, akin to Haglund's $(\mathsf{area ,hagbounce} )$ bistatistic on Dyck paths. In doing so, we have extended a bistatistic of Egge et al. to the set of parallelogram polyominoes. This is one answer to their question concerning extensions to other combinatorial objects. We conjecture the $q,t$-Narayana polynomials to be symmetric and discuss the proofs for numerous special cases. We also show a relationship between the $q,t$-Catalan polynomials and our bistatistic $(\mathsf{area ,parabounce}) $on a subset of parallelogram polyominoes.
In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements. Brieskorn (1971) showed that the fundamental group of the complement of the type W Coxeter arrangement (over $\mathbb{C}$) is isomorphic to the pure Artin group of type W. Khovanov (1996) gave an algebraic description for the fundamental group of the complement of the 3-equal arrangement (over $\mathbb{R}$). We generalize Khovanov's result to obtain an algebraic description of the fundamental group of the complement of the 3-parabolic arrangement for arbitrary finite reflection group. Our description is a real analogue to Brieskorn's description.
We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with respect to the number of ascents and occurrences of the pattern $13-2$, the generating function according to weak exceedances and crossings, and the $n^{\mathrm{th}}$ moment of certain $q$-Laguerre polynomials.
Let q be a prime a power and k an integer such that 3 ≤ k ≤ q. In this paper we present a method using Latin squares to construct adjacency matrices of k-regular bipartite graphs of girth 8 on 2(kq2 -- q) vertices. Some of these graphs have the smallest number of vertices among the known regular graphs with girth 8.
A breakthrough in the theory of (type $A$) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams. Recently, Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of the corresponding affine Weyl group. In this paper, we show that a Haglund-Haiman-Loehr type formula follows naturally from the more general Ram-Yip formula, via compression. Then we extend this approach to the Hall-Littlewood polynomials of type $C$, which are specializations of the corresponding Macdonald polynomials at $q=0$. We note that no analog of the Haglund-Haiman-Loehr formula exists beyond type $A$, so our work is a first step towards finding such a formula.
We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur functions that naturally generalizes the Pieri rule for Schur functions.
In this paper we consider the class of $\textit{permutominoes}$, i.e. a special class of polyominoes which are determined by a pair of permutations having the same size. We give a characterization of the permutations associated with convex permutominoes, and then we enumerate various classes of convex permutominoes, including parallelogram, directed-convex, and stack ones.
This paper provides a definition of a cellular line in a cellular array that is independent of the notion of a line in $\mathfrak{R}^2$.It also presents a way of determining whether or not a cell set is a cellular line.Brief statements about existence, uniqueness, and properties of cellular lines are included.
We investigate a scheduling problem in which packets, or datagrams, may be fragmented. While there are a few applications to scheduling with datagram fragmentation, our model of the problem is derived from a scheduling problem present in data over CATV networks. In the scheduling problem datagrams of variable lengths must be assigned (packed) into fixed length time slots. One of the capabilities of the system is the ability to break a datagram into several fragments. When a datagram is fragmented, extra bits are added to the original datagram to enable the reassembly of all the fragments. We convert the scheduling problem into the problem of bin packing with item fragmentation, which we define in the following way: we are asked to pack a list of items into a minimum number of unit capacity bins. Each item may be fragmented in which case overhead units are added to the size of every fragment. The cost associated with fragmentation renders the problem NP-hard, therefore an approximation algorithm is needed. We define a version of the well-known Next-Fit algorithm, capable of fragmenting items, and investigate its performance. We present both worst case and average case results and compare them to the case where fragmentation is not allowed.
This paper tackles the enumeration and asymptotics of the area below directed lattice paths (walks on $\mathbb{N}$ with a finite set of jumps). It is a nice surprise (obtained via the "kernel method'') that the generating functions of the moments of the area are algebraic functions, expressible as symmetric functions in terms of the roots of the kernel. For a large class of walks, we give full asymptotics for the average area of excursions ("discrete'' reflected Brownian bridge) and meanders ("discrete'' reflected Brownian motion). We show that drift is not playing any role in the first case. We also generalise previous works related to the number of points below a path and to the area between a path and a line of rational slope.