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It is known that connected sums of positive torus knots are not concordant to L-space knots. Here we consider differences of torus knots. The main result states that the subgroup of the concordance group generated by two positive torus knots contains no nontrivial L-space knots other than the torus knots themselves. Generalizations to subgroups generated by more than two torus knots are also considered. [ABSTRACT FROM AUTHOR]

Hom gives an example of a knot with vanishing Upsilon invariant but nonzero epsilon invariant. We build more such knots that are linearly independent in the smooth concordance group. [ABSTRACT FROM AUTHOR]

We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link L in S3. We then specialise this procedure to knots in S2 × S1 and obtain a lower bound on their geometric winding number. We then provide an infinite family of null-homologous knots with increasing geometric winding number on which the bound is sharp. [ABSTRACT FROM AUTHOR]

We investigate the disparity between smooth and topological almost concordance of knots in general 3-manifolds Y. Almost concordance is defined by considering knots in Y modulo concordance in Y × [0, 1] and the action of the concordance group of knots in S 3 that ties in local knots. We prove that the trivial free homotopy class in every 3-manifold other than the 3-sphere contains an infinite family of knots, all topologically concordant, but not smoothly almost concordant to one another. Then, in every lens space and for every free homotopy class, we find a pair of topologically concordant but not smoothly almost concordant knots. Finally, as a topological counterpoint to these results, we show that in every lens space every free homotopy class contains infinitely many topological almost concordance classes. [ABSTRACT FROM AUTHOR]

We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogenization of the Upsilon function, where Upsilon is the function-valued concordance homomorphism defined by Ozsváth, Stipsicz, and Szabó. We use this characterization to prove that n-braids with fractional Dehn twist coefficient larger than n - 1 realize the braid index of their closure. As a consequence, we are able to prove a conjecture of Malyutin and Netsvetaev stating that n-times twisted braids realize the braid index of their closure. We provide examples that address the optimality of our results. The paper ends with an appendix about the homogenization of knot concordance homomorphisms. [ABSTRACT FROM AUTHOR]

We show that a ribbon concordance between two links induces an injective map on Khovanov homology. [ABSTRACT FROM AUTHOR]

Cochran, Orr, and Teichner developed a filtration of the knot concordance group indexed by half integers called the solvable filtration. Its terms are denoted by Fn. It has been shown that Fn/Fn.5 is a very large group for n ≥ 0. For a generalization to the setting of links the third author showed that Fn.5/Fn+1 is non-trivial. In this paper we provide evidence for knots F0.5 = F1. In particular we prove that every genus 1 algebraically slice knot is 1-solvable. [ABSTRACT FROM AUTHOR]

In this paper, we combine the recent four-dimensional light bulb theorem of David Gabai and a construction of concordances for knots in S 2 × S 1 due to Eylem Zeliha Yildiz to construct an explicit concordance between the standard surface of genus g in S 2 × S 2 and any homologous surface using elementary methods. [ABSTRACT FROM AUTHOR]

We prove that for any winding number m > 0 pattern P and winding number -m pattern Q, there exist knots K such that the minimal genus of a cobordism between P(K) and Q(K) is arbitrarily large. This answers a question posed by Cochran-Harvey [Algebr. Geom. Topol. 18 (2018), pp. 2509-2540] and generalizes a result of Kim-Livingston [Pacific J. Math. 220 (2005), pp. 87-105]. [ABSTRACT FROM AUTHOR]

A virtual knot that has a homologically trivial representative 𝒦 in a thickened surface Σ × [ 0 , 1 ] is said to be an almost classical (AC) knot. 𝒦 then bounds a Seifert surface F ⊂ Σ × [ 0 , 1 ]. Seifert surfaces of AC knots are useful for computing concordance invariants and slice obstructions. However, Seifert surfaces in Σ × [ 0 , 1 ] are difficult to construct. Here, we introduce virtual Seifert surfaces of AC knots. These are planar figures representing F ⊂ Σ × [ 0 , 1 ]. An algorithm for constructing a virtual Seifert surface from a Gauss diagram is given. This is applied to computing signatures and Alexander polynomials of AC knots. A canonical genus of AC knots is also studied. It is shown to be distinct from the virtual canonical genus of Stoimenow–Tchernov–Vdovina. [ABSTRACT FROM AUTHOR]

Given a 3–manifold Y and a free homotopy class in [S¹, Y ], we investigate the set of topological concordance classes of knots in Y × [0, 1] representing the given homotopy class. The concordance group of knots in the 3–sphere acts on this set. We show in many cases that the action is not transitive, using two techniques. Our first technique uses Reidemeister torsion invariants, and the second uses linking numbers in covering spaces. In particular, we show using covering links that for the trivial homotopy class, and for any 3–manifold that is not the 3–sphere, the set of orbits is infinite. On the other hand, for the case that Y = S¹ × S², we apply topological surgery theory to show that all knots with winding number one are concordant. [ABSTRACT FROM AUTHOR]

Highlights • Piecewise model predicting sphere vertical distance and velocity time evolution upon vertical impact on liquid surface. • Model compared to experimental data for varying sphere mass ratios and impact velocities. • Additional model of cavity pinch-off confirmed to match experimental results well for full range of operating conditions. • Relatively simple model performs as well as complicated models; experimentally verified to deeper depths past pinch-off. • Light spheres affected by trailing cavity pinch-off and vortex ring formation for which the model does not account. Abstract This study presents a piecewise model for determining the vertical distance and velocity evolution with time for a sphere impacting a water surface and submerging to depths beyond deep-seal cavity pinch-off. Experimental data taken with a high-speed camera are presented for varying sphere mass ratios and impact velocities. The semi-empirical model incorporates results from previously published research and is shown to be in good agreement with experiments for heavier spheres but deviates when the sphere is only slightly denser than water. Two causes for the deviation are presented which relate to the dynamics of the cavity pinch-off event and the inception of a trailing vortex ring after the trailing cavity sloughs from the sphere. A model for predicting cavity pinch-off time and sphere position and velocity at the moment of cavity pinch-off is shown to agree well with experimental results for varying sphere mass ratios and impact velocities. The key experimental values are provided for comparison with current and future modeling efforts. [ABSTRACT FROM AUTHOR]

People spend most of their time indoors, thus maintaining a good indoor air quality (IAQ) is essential. To this end, one of the most effective methods to follow is the design of efficient ventilation; for this, the study of the local mean age of air (LMA) parameter is necessary. The objective of this research was to assess the influence of the presence of furniture, through validation of the numerical model CFD. The latter was implemented to calculate LMA in a room with two different furniture arrangements. Prior research on LMA calculation according to the arrangement of the furniture within an enclosure is not found in the literature. The tracer gas concentration decay method was used to develop the experimental analysis. The concordance between the data from the experimentation with those obtained in the numerical analysis was assessed. A greater difference was found in the values of the case with more furniture elements, although there was good agreement. In this study, the influence of the geometry of both the space and the furniture, and its arrangement in the room, on the efficiency of ventilation is shown. [ABSTRACT FROM AUTHOR]

Abstract: We establish a number of results about smooth and topological concordance of knots in S 1 × S 2. The winding number of a knot in S 1 × S 2 is defined to be its class in H 1 ( S 1 × S 2 ; Z ) ≅ Z. We show that there is a unique smooth concordance class of knots with winding number one. This improves the corresponding result of Friedl–Nagel–Orson–Powell in the topological category. We say a knot in S 1 × S 2 is slice (respectively, topologically slice) if it bounds a smooth (respectively, locally flat) disk in D 2 × S 2. We show that there are infinitely many topological concordance classes of non‐slice knots, and moreover, for any winding number other than ± 1, there are infinitely many topological concordance classes even within the collection of slice knots. Additionally, we demonstrate the distinction between the smooth and topological categories by constructing infinite families of slice knots that are pairwise topologically but not smoothly concordant, as well as non‐slice knots that are topologically slice and are pairwise topologically, but not smoothly, concordant. [ABSTRACT FROM AUTHOR]

Abstract: We give a method for constructing many pairs of distinct knots K 0 and K 1 such that the two 4‐manifolds obtained by attaching a 2‐handle to B 4 along K i with framing zero are diffeomorphic. We use the d‐invariants of Heegaard Floer homology to obstruct the smooth concordance of some of these K 0 and K 1, thereby disproving a conjecture of Abe. As a consequence, we obtain a proof that there exist patterns P in solid tori such that P ( K ) is not always concordant to P ( U ) # K and yet whose action on the smooth concordance group is invertible. [ABSTRACT FROM AUTHOR]

Abstract: We describe an action of the concordance group of knots in S 3 on concordances of knots in arbitrary 3‐manifolds. As an application we define the notion of almost‐concordance between knots. After some basic results, we prove the existence of non‐trivial almost‐concordance classes in all non‐abelian 3‐manifolds. Afterwards, we focus the attention on the case of lens spaces, and use a modified version of the Ozsváth–Szabó–Rasmussen's τ‐invariant to obstruct almost‐concordances and prove that each L ( p , 1 ) admits infinitely many nullhomologous non almost‐concordant knots. Finally we prove an inequality involving the cobordism P L‐genus of a knot and its τ‐invariants, in the spirit of [Sarkar, Math. Res. Lett. 18 (2011) 1239–1257]. [ABSTRACT FROM AUTHOR]

Abstract: We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many positive knots. [ABSTRACT FROM AUTHOR]

Let be the positively clasped untwisted Whitehead double of a knot , and be the torus knot. We show that and are linearly independent in the smooth knot concordance group for each . Further, and generate a summand in the subgroup of generated by topologically slice knots. We use the concordance invariant of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the -invariant of knot Floer theory and the -invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of for any generalizing a result for of Hedden, Kim and Livingston. [ABSTRACT FROM AUTHOR]

If a knot is a nontrivial connected sum of positive torus knots, then it is not concordant to an L-space knot. [ABSTRACT FROM AUTHOR]

We investigate the ultrasolvability problem for minimalp-group extensions of odd order: for the factorgroup of such extension, there exists a Galois extension of number fields such as corresponding embedding problem is ultrasolvable (i.e. this embedding problem is solvable and all its solutions are fields). [ABSTRACT FROM PUBLISHER]

We show that for each Seifert form of an algebraically slice knot with nontrivial Alexander polynomial, there exists an infinite family of knots having the Seifert form such that the knots are linearly independent in the knot concordance group and not concordant to any knot with coprime Alexander polynomial. Key ingredients for the proof are Cheeger-Gromov-von Neumann -invariants for amenable groups developed by Cha-Orr and polynomial splittings of metabelian -invariants. [ABSTRACT FROM AUTHOR]

We study concordance of virtual knots. Our main result is that a classical knot K is virtually slice if and only if it is classically slice. From this we deduce that the concordance group of classical knots embeds into the concordance group of long virtual knots. [ABSTRACT FROM AUTHOR]

Every classical knot is band-pass equivalent to the unknot or the trefoil. The band-pass class of a knot is a concordance invariant. Every ribbon knot, for example, is band-pass equivalent to the unknot. Here we introduce the long virtual knot concordance group . It is shown that for every concordance class , there is a that is not band-pass equivalent to and an that is not band-pass equivalent to either the long unknot or any long trefoil. This is accomplished by proving that is a band-pass invariant but not a concordance invariant of long virtual knots, where and generate the degree two Polyak group for long virtual knots. [ABSTRACT FROM AUTHOR]

To a special type of grope embedded in 4-space, that we call a branch-symmetric grope, we associate a length function for each real number [ABSTRACT FROM AUTHOR]

Neighbor-based collaborative ranking (NCR) techniques follow three consecutive steps to recommend items to each target user: first they calculate the similarities among users, then they estimate concordance of pairwise preferences to the target user based on the calculated similarities. Finally, they use estimated pairwise preferences to infer the total ranking of items for the target user. This general approach faces some problems and the rank data is usually sparse as users usually have compared only a few pairs of items. Consequently, the similarities among users is calculated based on limited information and is not accurate enough for inferring true values of preference concordance and can lead to an invalid ranking of items. This article presents a novel framework, called IteRank, that models the data as a bipartite network containing users and pairwise preferences. It then simultaneously refines users’ similarities and preferences’ concordances using a random walk method on this graph structure. It uses the information in this first step in another network structure for simultaneously adjusting the concordances of preferences and rankings of items. Using this approach, IteRank can overcome some existing problems caused by the sparsity of the data. Experimental results show that IteRank improves the performance of recommendation compared to the state of the art NCR techniques that use the traditional NCR framework for recommendation. [ABSTRACT FROM AUTHOR]

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs' evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

We study 3-braid knots of finite smooth concordance order. A corollary of our main result is that a chiral 3-braid knot of finite concordance order is ribbon. [ABSTRACT FROM AUTHOR]

Let β : = σ 1 σ 2 − 1 be a braid in B 3 , where B 3 is the braid group on 3 strings and σ 1 , σ 2 are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number n not divisible by 3 the knot which is represented by the closure of the braid β n is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers. [ABSTRACT FROM AUTHOR]

We give conditions ona⩾ −1,b∈ ( − ∞, ∞), andfandgso thatCa, b(x,y) =xy(1 +af(x)g(y))bis a bivariate copula. Many well-known copulas are of this form, including the Ali–Mikhail–Haq Family, Huang–Kotz Family, Bairamov–Kotz Family, and Bekrizadeh–Parham–Zadkarmi Family. One result is that we produce an algorithm for producing such copulas. Another is a one-parameter family of copulas whose measures of concordance range from 0 to 1. [ABSTRACT FROM AUTHOR]

We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature (upsc) outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up to concordance relative to the prescribed subset. We exhibit a general external product formula for partial secondary invariants, from which we deduce product formulas for the higher ?-invariant of a metric with upsc as well as for the higher relative index of two metrics with upsc. Our methods yield a new conceptual proof of the secondary partitioned manifold index theorem and a refined version of the delocalized Atiyah-Patodi-Singer (APS)-index theorem of Piazza-Schick for the spinor Dirac operator in all dimensions. We establish a partitioned manifold index theorem for the higher relative index. We also show that secondary invariants are stable with respect to direct products with aspherical manifolds that have fundamental groups of finite asymptotic dimension. Moreover, we construct examples of complete metrics with upsc on non-compact spin manifolds that can be distinguished up to concordance relative to subsets which are coarsely negligible in a certain sense. A technical novelty in this paper is that we use Yu's localization algebras in combination with the description of K-theory for graded C*-algebras due to Trout. This formalism allows direct definitions of all the invariants we consider in terms of the functional calculus of the Dirac operator and enables us to give concise proofs of the product formulas. [ABSTRACT FROM AUTHOR]

For consideration of the wide applications of concordance and order information in global sensitivity analysis (SA), a new sensitivity index based on the spearman correlation coefficient (S-CC) is presented in this article. S-CC can reflect the linear order correlation between variables; thus the proposed sensitivity index can be used to measure the influence of input on the linear order of output. Then the main task becomes efficiently estimating the defined index. Here the authors introduce the basic unscented transformation (UT) to compute the index with high efficiency, and high order unscented transformation (HOUT) is also employed tofurther improve the computational accuracy. Several examples, including the commonly used Ishigami test function and other engineering examples, are used to demonstrate the validity of the proposed sensitivity index and the efficiency of the proposed UT-based methods. [ABSTRACT FROM AUTHOR]

Each pattern P in a solid torus gives a function P : C ? C on the smooth knot concordance group, taking any knot K to its satellite P(K). We give examples of winding number one patterns P and a class of knots K, such that the iterated satellites Pi(K) are distinct in concordance, i.e. if i ≄ j = 0, Pi(K) ≄ Pj (K). This implies that the operators Pi give distinct functions on C, providing further evidence for the (conjectured) fractal nature of C. Our theorem also allows us to construct several sets of examples, such as infinite families of topologically slice knots that are distinct in smooth concordance, infinite families of 2-component links (with unknotted components and linking number one) which are not smoothly concordant to the positive Hopf link, and infinitely many prime knots which have the same Alexander polynomial as an L-space knot but are not themselves L-space knots. [ABSTRACT FROM AUTHOR]

We define a “reduced” version of the knot Floer complex CFK − ( K ) , and show that it behaves well under connected sums and retains enough information to compute Heegaard Floer d -invariants of manifolds arising as surgeries on the knot K . As an application to connected sums, we prove that if a knot in the three-sphere admits an L -space surgery, it must be a prime knot. As an application to the computation of d -invariants, we show that the Alexander polynomial is a concordance invariant within the class of L -space knots, and show the four-genus bound given by the d -invariant of +1-surgery is independent of the genus bounds given by the Ozsváth–Szabó τ invariant, the knot signature and the Rasmussen s invariant. [ABSTRACT FROM AUTHOR]

The concordance genus of a knot K is the minimum Seifert genus of all knots smoothly concordant to K. Concordance genus is bounded below by the 4-ball genus and above by the Seifert genus. We give a lower bound for the concordance genus of K coming from the knot Floer complex of K. As an application, we prove that there are topologically slice knots with 4-ball genus equal to 1 and arbitrarily large concordance genus. [ABSTRACT FROM AUTHOR]

The knot Floer complex and the concordance invariant e can be used to define a filtration on the smooth concordance group. We exhibit an ordered subset of this filtration that is isomorphic to N × N and consists of topologically slice knots. [ABSTRACT FROM AUTHOR]

Abstract: Combining known spectral sequences with a new spectral sequence relating reduced and unreduced -homology yields a relationship between the Homflypt-homology of a knot and its -concordance invariants. As an application, some of the -concordance invariants are shown to be linearly independent. [Copyright &y& Elsevier]

We give a sufficient condition under which the vanishing property of Cochran–Orr–Teichner knot concordance obstructions splits under connected sum. The condition is described in terms of self-annihilating submodules with respect to higher-order Blanchfield linking forms. This extends the results of Levine and the authors on distinguishing knots with coprime Alexander polynomials up to concordance. As an application, we show that the knots constructed by Cochran, Orr and Teichner as the first examples of nonslice knots with vanishing Casson–Gordon invariants are not concordant to any knots of genus one. This gives the first examples of concordance genus two knots with vanishing Casson–Gordon invariants. [ABSTRACT FROM PUBLISHER]

We show that if a link L with a non-zero Alexander polynomial admits a locally flat cobordism to a 'weakly m-split link', then the cobordism must have genus at least ｢m/2｣. This generalises a recent result of J. Pardon. [ABSTRACT FROM AUTHOR]

We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form can be converted into an unconstrained optimization problem. The relevant properties on the unconstrained optimization problem such as the duality, the boundedness of the solution and the path-following lemma, etc, are proved. Second, a self-concordant function on entire space which can be used as penalty for linear programming is constructed. For this specific function, more results are obtained. In particular, we show that, by taking a parameter large enough, the optimal solution for the unconstrained optimization problem is located in the increasing interval of the self-concordant function, which ensures the feasibility of solutions. Then by means of the self-concordant penalty function on entire space, a path-following algorithm on entire space for linear programming is presented. The number of Newton steps of the algorithm is no more than $$O(nL\log (nL/ {\varepsilon }))$$, and moreover, in short step, it is no more than $$O(\sqrt{n}\log (nL/{\varepsilon }))$$. [ABSTRACT FROM AUTHOR]

The concordance genus of a knot is the least genus of any knot in its concordance class. It is bounded above by the genus of the knot, and bounded below by the slice genus, two well-studied invariants. In this paper we consider the concordance genus of 11-crossing prime knots. This analysis resolves the concordance genus of 533 of the 552 prime 11-crossing knots. The appendix to the paper gives concordance diagrams for 59 knots found to be concordant to knots of lower genus, including null-concordances for the 30 11-crossing knots known to be slice. [ABSTRACT FROM AUTHOR]

We consider the question: "If the zero-framed surgeries on two oriented knots in S³ are Z-homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?" We show that this question has a negative answer in the smooth category, even for topologically slice knots. To show this we first prove that the zero-framed surgery on K is Z-homology cobordant to the zero-framed surgery on many of its winding number one satellites P(K). Then we prove that in many cases the T and s-invariants of K and P(K) differ. Consequently neither T nor s is an invariant of the smooth homology cobordism class of the zero-framed surgery. We also show that a natural rational version of this question has a negative answer in both the topological and smooth categories by proving similar results for K and its (p, 1)-cables. [ABSTRACT FROM AUTHOR]

Background. It is unclear whether history and physical examination findings can predict abnormalities on head computed tomography (CT) believed to indicate increased risk of lumbar-puncture- (LP-) induced brain herniation. The objectives of this study were to (1) identify head CT findings felt to be associated with increased risk of brain herniation and (2) to assess the ability of history and physical examination to predict those findings. Methods. Using a modified Delphi survey technique, an expert panel defined CT abnormalities felt to predict increased risk of LP-induced brain herniation. Presence of such findings on CT was compared with history and physical examination (H&P) variables in 47 patients. Results. No H&P variable predicted "high-risk" CT; combining H&P variables to improve sensitivity led to extremely low specificity and still failed to identify all patients with high-risk CT. Conclusions. "High-risk" CT is not uncommon in patients with clinical characteristics known to predict an absence of actual risk from LP, and thus it may not be clinically relevant. "Overdiagnosis" will be increasingly problematic as technological advances identify increasingly subtle deviations from "normal." [ABSTRACT FROM AUTHOR]