• Canada
• Publicationsclose
• LU close

Multimarginal Optimal Transport (MOT) has attracted significant interest due to applications in machine learning, statistics, and the sciences. However, in most applications, the success of MOT is severely limited by a lack of efficient algorithms. Indeed, MOT in general requires exponential time in the number of marginals k and their support sizes n. This paper develops a general theory about what "structure" makes MOT solvable in poly(n,k) time. We develop a unified algorithmic framework for solving MOT in poly(n,k) time by characterizing the "structure" that different algorithms require in terms of simple variants of the dual feasibility oracle. This framework has several benefits. First, it enables us to show that the Sinkhorn algorithm, which is currently the most popular MOT algorithm, requires strictly more structure than other algorithms do to solve MOT in poly(n,k) time. Second, our framework makes it much simpler to develop poly(n,k) time algorithms for a given MOT problem. In particular, it is necessary and sufficient to (approximately) solve the dual feasibility oracle -- which is much more amenable to standard algorithmic techniques. We illustrate this ease-of-use by developing poly(n,k) time algorithms for three general classes of MOT cost structures: (1) graphical structure; (2) set-optimization structure; and (3) low-rank plus sparse structure. For structure (1), we recover the known result that Sinkhorn has poly(n,k) runtime; moreover, we provide the first poly(n,k) time algorithms for computing solutions that are exact and sparse. For structures (2)-(3), we give the first poly(n,k) time algorithms, even for approximate computation. Together, these three structures encompass many -- if not most -- current applications of MOT. Comment: v4: to appear in Mathematical Programming, improved exposition and refs, no changes to technical results

Abstract We consider solutions of an initial value problem involving the equation ∂ 2 ∂t 2 (x,t)+ ∑ i=0 4 a i (x) ∂ i w ∂x i (x,t) ∑ i=0 2 b i (x) ∂ i+1 w ∂x i ∂t (x,t)=0 for x, t > 0. Here, a4(x) > 0 and is constant outside a compact set, b2(x) ⩽ 0, and the coefficients ai(x) for i ⩽ 3 and bi(x) for i ⩽ 2 vanish outside a compact set. We show that the solutions are given by an integral operator, the kernel of which is an infinitely differentiable function of t for t > 0. In fact, its derivatives satisfy Gevrey-2 bounds.

In this paper, we consider the existence of at least three positive solutions for the 2nth order differential equations with integral boundary conditions $$ \left \{ \textstyle\begin{array}{l} x^{(2n)}(t)=f(t, x(t), x''(t),\ldots,x^{(2(n-1))}(t)), \quad 0\leq t\leq 1, \\ x^{(2i)}(0)=\int_{0}^{1}k_{i}(s)x^{(2i)}(s) \,\mathrm{d}s,\qquad x^{(2i)}(1)=0, \quad 0\leq i\leq n-1, \end{array}\displaystyle \right . $$ where $(-1)^{n}f>0$ is continuous, and $k_{i}(t)\in L^{1}[0,1]$ ( $i=0,1,\ldots,n-1$ ) are nonnegative. The associated Green’s function for the higher order differential equations with integral boundary conditions is first given, and growth conditions are imposed on f which yield the existence of multiple positive solutions by using the Leggett-Williams fixed point theorem.

Background and PurposeChemokines and their receptors form an intricate interaction and signalling network that plays critical roles in various physiological and pathological cellular processes. The high promiscuity and apparent redundancy of this network makes probing individual chemokine/receptor interactions and functional effects, as well as targeting individual receptor axes for therapeutic applications, challenging. Despite poor sequence identity, the N‐terminal regions of chemokines, which play a key role in their activity and selectivity, contain several conserved features. Thus far little is known regarding the molecular basis of their interactions with typical and atypical chemokine receptors or the conservation of their contributions across chemokine‐receptor pairs.Experimental ApproachWe used a broad panel of chemokine variants and modified peptides derived from the N‐terminal region of chemokines CXCL12, CXCL11 and vCCL2, to compare the contributions of various features to binding and activation of their shared receptors, the two typical, canonical G protein‐signalling receptors, CXCR4 and CXCR3, as well as the atypical scavenger receptor CXCR7/ACKR3, which shows exclusively arrestin‐dependent activity.Key ResultsWe provide molecular insights into the plasticity of the ligand‐binding pockets of these receptors, their chemokine binding modes and their activation mechanisms. Although the chemokine N‐terminal region is a critical determinant, neither the most proximal residues nor the N‐loop are essential for binding and activation of ACKR3, as distinct from binding and activation of CXCR4 and CXCR3.Conclusion and ImplicationsThese results suggest a different interaction mechanism between this atypical receptor and its ligands and illustrate its strong propensity to activation.

OBJECTIVE: To assess the prevalence of underweight (UW), overweight (OW), and obesity in children and adolescents with type 1 diabetes (T1D).METHODS: An international cross-sectional study including 23 026 T1D children (2-18 years, duration of diabetes ≥1 year) participating in the SWEET prospective, multicenter diabetes registry. Body mass index SD score (BMI-SDS) was calculated using the World Health Organization BMI charts. Children were categorized as UW (BMI-SDS < -2SD), OW (+1SD < BMI-SDS ≤ +2SD), and obese (OB) (BMI-SDS > +2SD). Hierarchic regression models were applied with adjustment for sex, age, and duration of diabetes.RESULTS: The prevalence of UW, OW, and obesity was: 1.4%, 22.3%, and 7.3% in males and 0.6%, 27.2%, and 6.8% in females. Adjusted BMI-SDS was significantly higher in females than in males (mean ± SEM: 0.54 ± 0.05 vs 0.40 ± 0.05, P < 0.0001). In males, BMI-SDS significantly decreased by age (P < 0.0001) in the first three age categories 0.61 ± 0.06 (2 to <10 years), 0.47 ± 0.06 (10 to <13 years), 0.34 ± 0.05 (13 to <16 years). In females, BMI-SDS showed a U-shaped distribution by age (P < 0.0001): 0.54 ± 0.04 (2 to <10 years), 0.39 ± 0.04 (10 to <13 years), 0.55 ± 0.04 (13 to <16 years). BMI-SDS increased by diabetes duration (<2 years: 0.38 ± 0.05, 2 to <5 years: 0.44 ± 0.05, and ≥5 years: 0.50 ± 0.05, P < 0.0001). Treatment modality did not affect BMI-SDS. Adjusted HbA1c was significantly higher in females than in males (8.20% ± 0.10% vs 8.06% ± 0.10%, P < 0.0001). In both genders, the association between HbA1c and BMI-SDS was U-shaped with the highest HbA1c in the UW and obesity groups.CONCLUSIONS: The high rate of OW and obesity (31.8%) emphasize the need for developing further strategies to prevent and treat excess fat accumulation in T1D.

Abstract Cross-country research finds mixed performance effects of family involvement in management (FIM) but consistently positive performance effects of family involvement in ownership (FIO). We argue that cross-country differences in institutional trust and trust in family can help explain this discrepancy. We reason that trust in family normalizes family managers’ use of firm resources to satisfy family needs. In contrast, institutional trust orientates family managers’ attention toward improving firm performance. A meta-analysis supports our theory: greater trust in family increases and greater institutional trust reduces the gap between FIM and FIO's performance effects across countries.

Confronted with negative environmental impacts, rising fuel costs and increas-ing congestion, many cities are implementing sustainable mobility measures to improve the flow of passenger and goods. Examples of these measures are use of public transport, cycling, walking, energy efficient vehicles, biofuels. The challenge before transport decision makers is which one(s) to choose for im-plementation as often there is no or limited quantitative data available on the subject. Moreover, the context of each city, its geographic and transport condi-tions restrict the generalization of results obtained in experienced cities. In this paper, we investigate four multicriteria decision making (MCDM) techniques namely TOPSIS, VIKOR, SAW and GRA for sustainability evaluation of urban mobility projects under qualitative data and demonstrate their application through a numerical example.