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Background: Weight recurrence, suboptimal clinical response and functional disorder (such as reflux) after a Sleeve Gastrectomy (SG) are problems that may require conversional surgery. For reflux, conversion to Roux-en-Y Gastric Bypass (RYGB) is considered effective. Regarding treatment for suboptimal clinical response, the technique of choice remains a subject of debate. This study aims to evaluate the safety and effectiveness of conversion from SG to Ring-augmented RYGB (RaRYGB). Methods: All laparoscopic SG to RaRYGB conversions performed between January 2016 and January 2022 were included. Primary outcome was percentage total weight loss (%TWL) after 1-year follow-up. Secondary outcomes consisted of cumulative %TWL, complications (with a focus on ring-related complications), and resolution of medical-associated problems. Results: We included 50 patients of whom 44 were female. Mean pre-conversion BMI was 37.6 kg/m2. All patients have reached the 1-year follow-up point, however 10 were lost to follow-up. After 1-year mean TWL was 17.8% while mean cumulative TWL, calculated from primary SG, was 32%. A total of 10 complications occurred in 8 patients within 30 days, 6 of which were ≤ CD3a and 4 ≥ CD3b. One MiniMizer was removed for complaints of severe dysphagia. Of the 35 medical-associated problems present at screening 5 remained unchanged(14.2%), 15 improved(42.9%) and 15 achieved remission(42.9%). Conclusion: Our series of 50 patients undergoing conversion from SG to RaRYGB is adequate and successful regarding additional weight loss 1 year after conversion, cumulative weight loss, complication rate and achievement of improvement or remission of medical-associated problems. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence, boundedness, and integrability of minimizers of heterogeneous, two-phase free boundary problems Jγ(u) = ∫Ω (f(x, ∇u) + λ+(u+)γ + λ−(u−)γ + gu) dx → min under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with γ = 0, chemical reaction problems with 0 < γ < 1, and obstacle type problems with γ = 1, respectively. [ABSTRACT FROM AUTHOR]

We consider the functional ℱ(u)≔∫Ωf(x,Du(x))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }f\left(x,Du\left(x)){\rm{d}}x, where f(x,z)f\left(x,z) satisfies a (p,q)\left(p,q)-growth condition with respect to zz and can be approximated by means of a suitable sequence of functions. We consider BR⋐Ω{B}_{R}\hspace{0.33em}\Subset \hspace{0.33em}\Omega and the spaces X=W1,p(BR,RN)andY=W1,p(BR,RN)∩Wloc1,q(BR,RN).X={W}^{1,p}\left({B}_{R},{{\mathbb{R}}}^{N})\hspace{1.0em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{1.0em}Y={W}^{1,p}\left({B}_{R},{{\mathbb{R}}}^{N})\cap {W}_{\hspace{0.1em}\text{loc}\hspace{0.1em}}^{1,q}\left({B}_{R},{{\mathbb{R}}}^{N}). We prove that the lower semicontinuous envelope of ℱ∣Y{\mathcal{ {\mathcal F} }}{| }_{Y} coincides with ℱ{\mathcal{ {\mathcal F} }} or, in other words, that the Lavrentiev term is equal to zero for any admissible function u∈W1,p(BR,RN)u\in {W}^{1,p}\left({B}_{R},{{\mathbb{R}}}^{N}). We perform the approximations by means of functions preserving the values on the boundary of BR{B}_{R}.

This paper deals with regularity properties for variational integrals with the splitting structure of the form J(u,Ω)=∫Ω∑i=1n+1fi(x,Dui)+gi(x,(adjnDu)i)dx,$$\begin{equation*} \hspace*{59pt}{\cal J} (u,\Omega) = \int _{\Omega } \sum _{i=1}^{n+1} {\left\lbrace f^{i}(x,Du^{i})+ g^{i}(x,({\rm adj} _{n}Du)^{i}) \right\rbrace} dx, \end{equation*}$$where u=(u1,u2,…,un+1):Ω⊂Rn→Rn+1$u=(u^1,u^2, \ldots, u^{n+1}):\Omega \subset \mathbb {R}^n \rightarrow \mathbb {R}^{n+1}$, adjnDu∈Rn+1${\rm adj}_n Du \in \mathbb {R}^{n+1}$ is the adjugate matrix of order n$n$, and fi:Ω×Rn→R$f^i:\Omega \times \mathbb {R}^{n} \rightarrow \mathbb {R}$, gi:Ω×R→R$g^i:\Omega \times \mathbb {R} \rightarrow \mathbb {R}$, i=1,2,…,n+1$i=1,2, \ldots, n+1$, are Carathéodory functions satisfying suitable structural conditions. Local integrability, local boundedness, and local Hölder continuity for local minimizers are derived. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of L 2 -norm solutions for the related equation when the potential function V (x) fulfills an appropriate choice. [ABSTRACT FROM AUTHOR]

In this paper, we establish regularity results for local minimizers of functionals with non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integral with two modulating coefficients w ↦ ∫ [ a (x) | D w | p + b (x) | D w | q ] d x , 1 < p < q , a (·) , b (·) ≥ 0 , with 0 < μ ≤ a (·) + b (·) . Here, the coefficient b (·) is assumed to be Hölder continuous and the coefficient a (·) is assumed to be uniformly continuous. [ABSTRACT FROM AUTHOR]

This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals $\Phi(u)=\int_a^b f(x,u(x),u'(x))\,dx$, where $u\in C^1([a,b],{\mathbb R}^N)$. We first derive conditions which are simpler than the known ones, and then apply them to several particular problems, including stability problems in the elasticity theory. In particular, we solve some open problems in [A. Majumdar, A. Raisch: Stability of twisted rods, helices and buckling solutions in three dimensions, Nonlinearity 27(2014), 2841–2867] by finding optimal conditions for the stability of a naturally straight Kirchhoff rod under various types of endpoint constraints.

Given a unit vector v ∈ R 3 and λ ∈ R , a translating λ -soliton is a surface in R 3 whose mean curvature H satisfies H = ⟨ N , v ⟩ + λ , where N is the Gauss map of the surface. In this paper, we extend the phenomenon of instability of Plateau–Rayleigh for translating λ -solitons of cylindrical type, proving that long pieces of these surfaces are unstable. Specifically, we will provide explicit bounds on the length of these unstable surfaces in terms of λ and the amplitude of the generating curve. It will be also proved that a graphical translating λ -soliton is a minimizer of the weighted area in a suitable class of surfaces with the same boundary and the same weighted volume. [ABSTRACT FROM AUTHOR]

We prove the absence of the Lavrentiev gap for non-autonomous functionals ℱ ⁢ (u) ≔ ∫ Ω f ⁢ (x , D ⁢ u ⁢ (x)) ⁢ 푑 x , where the density f ⁢ (x , z) is α-Hölder continuous with respect to x ∈ Ω ⊂ ℝ n , it satisfies the (p , q) -growth conditions | z | p ⩽ f ⁢ (x , z) ⩽ L ⁢ (1 + | z | q) , where 1 < p < q < p ⁢ (n + α n) , and it can be approximated from below by suitable densities f k . [ABSTRACT FROM AUTHOR]

The amount of sequencing data for SARS-CoV-2 is several orders of magnitude larger than any virus. This will continue to grow geometrically for SARS-CoV-2, and other viruses, as many countries heavily finance genomic surveillance efforts. Hence, we need methods for processing large amounts of sequence data to allow for effective yet timely decision-making. Such data will come from heterogeneous sources: aligned, unaligned, or even unassembled raw nucleotide or amino acid sequencing reads pertaining to the whole genome or regions (e.g., spike) of interest. In this work, we propose ViralVectors, a compact feature vector generation from virome sequencing data that allows effective downstream analysis. Such generation is based on minimizers, a type of lightweight "signature" of a sequence, used traditionally in assembly and read mapping — to our knowledge, the first use minimizers in this way. We validate our approach on different types of sequencing data: (a) 2.5M SARS-CoV-2 spike sequences (to show scalability); (b) 3K Coronaviridae spike sequences (to show robustness to more genomic variability); and (c) 4K raw WGS reads sets taken from nasal-swab PCR tests (to show the ability to process unassembled reads). Our results show that ViralVectors outperforms current benchmarks in most classification and clustering tasks. Graphical Abstract showing the all steps of proposed approach. We start by collecting the sequence-based data. Then Data cleaning and preprocessing is applied. After that, we generate the feature embeddings using minimizer based approach. Then Classification and clustering algorithms are applied on the resultant data and predictions are made on the test set. [ABSTRACT FROM AUTHOR]

Given certain set $ \mathcal{K} $ and functions $ q $ and $ h $, we study geometric properties of the set $ \partial\{x\in\Omega:u(x) > 0\} $ for non-negative minimizers of the functional $ \mathcal{J} (u) = \int_{\Omega }^{} \, \left(\frac{1}{p}| \nabla u| ^p+q(u^+)^\gamma +hu\right)\text{d}x $ over $ \mathcal{K} $, where $ {\Omega \subset} \mathbb{R} ^n(n\geq 2) $ is an open bounded domain, $ p\in(1, +\infty) $ and $ \gamma \in (0, 1] $ are constants, $ u^+ $ is the positive part of $ u $ and $ \partial\{x\in\Omega :u(x) > 0\} $ is the so-called free boundary. Such a minimum problem arises in physics and chemistry for $ \gamma = 1 $ and $ \gamma \in(0, 1) $, respectively. Using the comparison principle of $ p $-Laplacian equations, we establish first the non-degeneracy of non-negative minimizers near the free boundary, then prove the local porosity of the free boundary.

Abstract In the present paper, we consider the existence of solutions with a prescribed l 2 $l^{2}$ -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f ( u k ) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , $$ \textstyle\begin{cases} -\Delta ^{2} u_{k-1}-f(u_{k})= \lambda u_{k} \quad k\in \mathbb{Z}, \\ \sum_{k\in \mathbb{Z}} \vert u_{k} \vert ^{2}=\alpha ^{2}, \end{cases} $$ where Δ 2 u k − 1 = u k + 1 + u k − 1 − 2 u k $\Delta ^{2} u_{k-1}=u_{k+1}+u_{k-1}-2u_{k}$ , f ∈ C ( R ) $f\in C(\mathbb{R}) $ , α is a fixed constant, and λ ∈ R $\lambda \in \mathbb{R}$ arises as a Lagrange multiplier. To get the solutions, we investigate the corresponding minimizing problem with the l 2 $l^{2}$ -norm constraint: E α = inf { 1 2 ∑ | Δ u k − 1 | 2 − ∑ F ( u k ) : ∑ | u k | 2 = α 2 } . $$ E_{\alpha}=\inf \biggl\{ \frac{1}{2}\sum \vert \Delta u_{k-1} \vert ^{2}-\sum F(u_{k}): \sum \vert u_{k} \vert ^{2}=\alpha ^{2} \biggr\} . $$ An elaborative analysis on a minimizing sequence with respect to E α $E_{\alpha}$ is obtained. We prove that there is a constant α 0 ≥ 0 $\alpha _{0}\geq 0$ such that there exists a global minimizer if α > α 0 $\alpha >\alpha _{0}$ , and there exists no global minimizer if α < α 0 $\alpha

This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of L2-norm solutions for the related equation when the potential function V(x) fulfills an appropriate choice.

Abstract Genomics analyses use large reference sequence collections, like pangenomes or taxonomic databases. SPUMONI 2 is an efficient tool for sequence classification of both short and long reads. It performs multi-class classification using a novel sampled document array. By incorporating minimizers, SPUMONI 2’s index is 65 times smaller than minimap2’s for a mock community pangenome. SPUMONI 2 achieves a speed improvement of 3-fold compared to SPUMONI and 15-fold compared to minimap2. We show SPUMONI 2 achieves an advantageous mix of accuracy and efficiency in practical scenarios such as adaptive sampling, contamination detection and multi-class metagenomics classification.

Given certain set K and functions q and h , we study geometric properties of the set ∂ { x ∈ Ω : u (x) > 0 } for non-negative minimizers of the functional J (u) = ∫ Ω (1 p | ∇ u | p + q (u +) γ + h u) d x over K , where Ω ⊂ R n (n ≥ 2) is an open bounded domain, p ∈ (1 , + ∞) and γ ∈ (0 , 1 ] are constants, u + is the positive part of u and ∂ { x ∈ Ω : u (x) > 0 } is the so-called free boundary. Such a minimum problem arises in physics and chemistry for γ = 1 and γ ∈ (0 , 1) , respectively. Using the comparison principle of p -Laplacian equations, we establish first the non-degeneracy of non-negative minimizers near the free boundary, then prove the local porosity of the free boundary. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the following Kirchhoff equation where Ω ⊂ R 3 is a bounded connected domain and ∫ Ω | u | 2 d x = 1 . The results of existence and nonexistence on L 2 -norm solutions are given. Our argument shows that the blow-up behavior of L 2 -norm solution occurs, and the mass concentrates at an inner point of Ω , or the neighborhood of some boundary point. [ABSTRACT FROM AUTHOR]

The weak lower semicontinuity of the functional ... is a classical topic that was studied thoroughly. It was shown that if the function f is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on W1,p(Ω). However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the existence of solutions with a prescribed l 2 -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f (u k) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , where Δ 2 u k − 1 = u k + 1 + u k − 1 − 2 u k , f ∈ C (R) , α is a fixed constant, and λ ∈ R arises as a Lagrange multiplier. To get the solutions, we investigate the corresponding minimizing problem with the l 2 -norm constraint: E α = inf { 1 2 ∑ | Δ u k − 1 | 2 − ∑ F (u k) : ∑ | u k | 2 = α 2 }. An elaborative analysis on a minimizing sequence with respect to E α is obtained. We prove that there is a constant α 0 ≥ 0 such that there exists a global minimizer if α > α 0 , and there exists no global minimizer if α < α 0 . It seems that it is the first time to consider the solution with a prescribed l 2 -norm of the discrete Schrödinger equations. [ABSTRACT FROM AUTHOR]

We study a variational approach introduced by S.D. Fisher and the author in the 1970s in the context of norm minimization for differentiable mappings occurring in nonlinear elliptic boundary value problems. It may be viewed as an abstract version of the calculus of variations. A strong hypothesis, initially limiting the scope of this approach, is the assumption of a bounded minimizing sequence in the least squares formulation. In this article, we employ regularization and invariant regions to overcome this obstacle. A consequence of the framework is the convergence of approximations for regularized problems to a desired solution. The variational method is closely associated with the implicit function theorem, and it can be jointly studied, so that continuous parameter stability is naturally deduced. A significant aspect of the theory is that the reaction term in a reaction-diffusion equation can be selected to act globally as in the steady Schrödinger-Hartree equation. Local action, as in the non-equilibrium Poisson-Boltzmann equation, is also included. Both cases are studied at length prior to the development of a general theory. [ABSTRACT FROM AUTHOR]

In this paper we establish boundedness and continuity results for vectorial local minimizers of special classes of integral functionals. In particular we consider a class of vectorial problems in which the energy density satisfies fully anisotropic growth. We analyze two different types of anisotropic growths connected with the Orlicz Sobolev spaces. We prove boundedness results for energy densities satisfying anisotropic growth, moreover for particular energy densities we get Hölder continuity results by proving that each component belongs to a suitable De Giorgi class. Finally, we provide specific non-trivial instances of our results. [ABSTRACT FROM AUTHOR]

In this paper we study the everywhere Hölder continuity of the minima of the following class of vectorial integral functionals ∫ Ω ∑ α = 1 n f α x , u α , ∇ u α + G x , u , ∇ u d x The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. [ABSTRACT FROM AUTHOR]

A way to measure the lower growth rate of φ:Ω×[0,∞)→[0,∞)$$ \varphi :\Omega \times \left[0,\infty \right)\to \left[0,\infty \right) $$ is to require t↦φ(x,t)t−r$$ t\mapsto \varphi \left(x,t\right){t}^{-r} $$ to be increasing in (0,∞)$$ \left(0,\infty \right) $$. If this condition holds with r=1$$ r=1 $$, then infu∈f+W01,φ(Ω)∫Ωφ(x,|∇u|)dx$$ \underset{u\in f+{W}_0^{1,\varphi}\left(\Omega \right)}{\operatorname{inf}}{\int}_{\Omega}\varphi \left(x,|\nabla u|\right)\kern0.1em dx $$ with boundary values f∈W1,φ(Ω)$$ f\in {W}^{1,\varphi}\left(\Omega \right) $$ does not necessarily have a minimizer. However, if φ$$ \varphi $$ is replaced by φp$$ {\varphi}^p $$, then the growth condition holds with r=p>1$$ r=p>1 $$ and thus (under some additional conditions) the corresponding energy integral has a minimizer. We show that a sequence (up)$$ \left({u}_p\right) $$ of such minimizers converges when p→1+$$ p\to {1}^{+} $$ in a suitable BV$$ \mathrm{BV} $$‐type space involving generalized Orlicz growth and obtain the Γ$$ \Gamma $$‐convergence of functionals with fixed boundary values and of functionals with fidelity terms. [ABSTRACT FROM AUTHOR]

Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a (p , q) -Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents p and q. The setting is a doubling metric measure space supporting a Poincaré inequality. [ABSTRACT FROM AUTHOR]

In the present paper, we study a class of discrete Schrödinger equations with concave–convex nonlinear terms via the variational method. Under certain conditions on the nonlinearities, two nontrivial solutions of the equations have been obtained by finding the minimizers on Nehari manifolds, and one of them is the ground state solution with negative energy. As we all know, there are few results on discrete systems involving concave–convex nonlinearities. [ABSTRACT FROM AUTHOR]

Purpose: Development of an algorithm to self-calibrate arbitrary CBCT trajectories which can be used to reduce metal artifacts. By using feature detection and matching we want to reduce the amount of parameters for the BFGS optimization and thus reduce the runtime. Methods: Each projection is 2D-3D registered on a prior image with AKAZE feature detection and brute force matching. Translational misalignment is calculated directly from the misalignment of feature positions, rotations are aligned using a minimization algorithm that fits a quartic function and determines the minimum of this function. Evaluation: We did three experiments to compare how well the algorithm can handle noise on the different degrees of freedom. Our algorithms are compared to Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimizer with Normalized Gradient Information (NGI) objective function, and BFGS with distance between features objective function using SSIM, nRMSE, and the Dice coefficient of segmented metal object. Results: Our algorithm (Feature ORiented Calibration for Arbitrary Scan Trajectories with Enhanced Reliability (FORCASTER)) performs on par with the state-of-the-art algorithms (BFGS with NGI objective). nRMSE: FORCASTER = 0.3390, BFGS+NGI = 0.3441; SSIM: FORCASTER = 0.83, BFGS + NGI = 0.79; Dice: FORCASTER = 0.86, BFGS + NGI = 0.87. Conclusion: The proposed algorithm can determine the parameters of the projection orientations for arbitrary trajectories with calibration quality comparable to state-of-the-art algorithms, but faster and with higher tolerance to errors in the initially guessed parameters. [ABSTRACT FROM AUTHOR]

We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometric rigidity of complete Riemannian manifolds admitting local minimizers of energy functionals. More precisely, assuming the existence of a non-trivial local minimizer and under suitable assumptions, a Riemannian manifold under consideration must be a product manifold furnished with a warped metric. Secondly, under similar hypotheses, we deduce a geometrical splitting in the same fashion as in the Cheeger–Gromoll splitting theorem and we also get information about local minimizers. [ABSTRACT FROM AUTHOR]

We show that the Weierstrass–Hilbert classical field theory can be strengthened. Namely, for each extremal field, it is true that if an extremal is an element of the field then a minimum is attained in the class of Sobolev functions with the same boundary data as for the extremal and with graphs in the set covered by the field. This result remains valid if one of the extremals is singular. If there is a field containing more than one singular extremal then each of these extremals defines the minimization problem having no solution in the class of Lipschitz functions with graphs in the set covered by the field. [ABSTRACT FROM AUTHOR]

We give conditions for the convergence of minimizers and minimum values of integral and more general functionals J s : W 1 , p (Ω s) → R on sets of functions defined by a measurable lower constraint φ : Ω → R ¯ and a measurable upper constraint ψ : Ω → R ¯ , where Ω is a bounded domain in R n ( n ⩾ 2 ), { Ω s } is a sequence of domains in R n contained in Ω , and p > 1 . These conditions include the Γ -convergence of the functionals under consideration and some requirements on the domains Ω s . As for the constraints φ and ψ , we consider two cases. In the first case, we assume that there exist functions φ ¯ , ψ ¯ ∈ W 1 , p (Ω) such that φ ⩽ φ ¯ < ψ ¯ ⩽ ψ a.e. in Ω . In the second case, we assume that there exists a function β ∈ W 1 , p (Ω) satisfying the inequality φ ⩽ β ⩽ ψ a.e. in Ω and interacting with the integrands of the main components of the functionals J s in a special way. [ABSTRACT FROM AUTHOR]

Given certain functions φ , q , h and a nonnegative constant λ , we establish regularities for the free boundary problem J (u) = ∫ Ω (G (| ∇ u |) + q F (u +) + h u + λ χ { u > 0 } ) d x → min , over the set { u ∈ W 1 , G (Ω) : u - φ ∈ W 0 1 , G (Ω) } in the setting of Orlicz spaces, where the functions G and F satisfy the structural conditions of Tolksdorf's type. Moreover, F allows for subcritical exponents. The main results obtained in this paper include: the local C 1 , α - and Log-Lipschitz continuities of minimizers in the subcritical case for λ = 0 and λ ≥ 0 , respectively; the growth rates near the free boundary for non-negative minimizers in the subcritical case for λ ≥ 0 , which give the optimal growth rates of non-negative minimizers for the p-Laplacian problems; the local Lipschitz continuity of non-negative minimizers for λ > 0 under the natural growth condition that F (t) ≲ 1 + G (t) for t ≥ 0 . All the results presented in this paper are new even for the free boundary problems of p-Laplacian. [ABSTRACT FROM AUTHOR]

Support vector machines with ramp loss ( L r -SVM) have attracted considerable attention due to the robustness of the ramp loss. However, the corresponding optimization problem is non-convex, and the given Karush–Kuhn–Tucker (KKT) conditions are only first-order necessary conditions. To enrich the optimality theory of L r -SVM, we first introduce and analyze the proximal operator for the ramp loss, and then establish a stronger optimality condition: P-stationarity, which is proved to be the first-order necessary and sufficient conditions for the local minimizer of L r -SVM. Finally, we define the P-support vectors based on the P-stationary point and show that under mild conditions, all of the P-support vectors for L r -SVM are on the two support hyperplanes. [ABSTRACT FROM AUTHOR]

We study minimizers of the Dirichlet φ‐energy integral with generalized Orlicz growth. We prove the Kellogg property, the set of irregular points has zero capacity, and give characterizations of semiregular boundary points. The results are new ever for the special cases double phase and Orlicz growth. [ABSTRACT FROM AUTHOR]

National recommendations allow for the omission of sentinel lymph node biopsy (SLNB) and post-lumpectomy radiotherapy in women ≥ 70 y/o with early-stage, hormone-receptor positive invasive breast cancer, but these therapies remain common. Previous work demonstrates an individual's maximizing-minimizing trait—an inherent preference for more or less medical care—may influence the preference for low-value care. We recruited an equal number of women ≥ 70 yrs who were maximizers, minimizers, or neutral based on a validated measure between September 2020 and November 2020. Participants were presented a hypothetical breast cancer diagnosis before randomization to one of three follow-up messages: maximizer-tailored, minimizer-tailored, or neutral. Tailored messaging aimed to redirect maximizers and minimizers toward declining SLNB and radiotherapy. The main outcome measure was predicted probability of choosing SLNB or radiotherapy. The final analytical sample (n = 1600) was 515 maximizers (32%), 535 neutral (33%) and 550 (34%) minimizers. Higher maximizing tendency positively correlated with electing both SLNB and radiotherapy on logistic regression (P < 0.01). Any tailoring (maximizer- or minimizer-tailored) reduced preference for SLNB in maximizing and neutral women but had no effect in minimizing women. Tailoring had no impact on radiotherapy decision, except for an increased probability of minimizers electing radiotherapy when presented with maximizer-tailored messaging. Maximizing-minimizing tendencies are associated with treatment preferences among women facing a hypothetical breast cancer diagnosis. Targeted messaging may facilitate avoidance of low-value breast cancer care, particularly for SLNB. [ABSTRACT FROM AUTHOR]

In this article, we study the Schrödinger–Newton equations − Δ u + 2 π φ u = μ u + | u | p u , i n R 2 , Δ φ = u 2 , i n R 2. We prove the existence of positive spherically symmetric decreasing solutions for p ∈ (0 , 2) by constrained minimization methods. For p = 2, by the Gagliardo–Nirenberg inequality, an elaborate estimate implies similar existence results. We also give the regularity, exponential decay and blow-up behavior of these solutions. [ABSTRACT FROM AUTHOR]

The extended Painlevé P.D.E. system Δ y − x 1 y − 2 | y | 2 y = 0 , (x 1 , ... , x n) ∈ R n , y : R n → R m , is obtained by multiplying by − x 1 the linear term of the Ginzburg-Landau equation Δ η = | η | 2 η − η , η : R n → R m. The two dimensional model n = m = 2 describes in the theory of light-matter interaction in liquid crystals, the orientation of the molecules at the boundary of the illuminated region. On the other hand, the one dimensional model reduces to the second Painlevé O.D.E. y ″ − x y − 2 y 3 = 0 , x ∈ R , which has been extensively studied, due to its importance for applications. The solutions of the extended Painlevé P.D.E. share some characteristics both with the Ginzburg-Landau equation and the second Painlevé O.D.E. The scope of this paper is to construct vortex-filament solutions y : R n → R n − 1 (∀ n ≥ 3) of the extended Painlevé equation. These solutions have in every hyperplane x 1 = Const. , a profile similar to the standard vortices η : R n − 1 → R n − 1 of the Ginzburg-Landau equation, but their amplitude is determined by the Hastings-McLeod solution h of the second Painlevé O.D.E. evaluated at x 1. [ABSTRACT FROM AUTHOR]

Using a variational approach we study interior regularity for quasiminimizers of a (p, q)-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally Hölder continuous and they satisfy Harnack inequality, the strong maximum principle and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for Hölder continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we consider (p, q)-minimizers and we give an estimate for their oscillation at boundary points. [ABSTRACT FROM AUTHOR]

Consider the recovery of the weight function in distributed time-fractional diffusion system using the interior measurement, which arises in some ultra-slow diffusion phenomena. Due to the nonlinear and nonlocal dependance of the measurement data on the weight function, such an inverse problem is novel and important. Based on the regularities of the direct problems for general diffusion equations with distributed time fractional derivative shown in this paper, we establish the theoretical framework for the optimization version of the inverse problem, including existence of the minimizer, the differentiability of the cost functional, as well as the gradient of the cost functional, in suitable functional spaces. Then an iteration process of descent type is realized efficiently for minimizing the regularizing cost functional in terms of the gradient type iteration, with numerical examples showing the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract Background Seeding is usually the initial step of high-throughput sequence aligners. Two popular seeding strategies are fixed-size seeding (k-mers, minimizers) and variable-size seeding (MEMs, SMEMs, maximal spanning seeds). The former strategy supports fast seed computation, while the latter one benefits from a high seed uniqueness. Algorithmic bridges between instances of both seeding strategies are of interest for combining their respective advantages. Results We introduce an efficient strategy for computing MEMs out of fixed-size seeds (k-mers or minimizers). In contrast to previously proposed extend-purge strategies, our merge-extend strategy prevents the creation and filtering of duplicate MEMs. Further, we describe techniques for extracting SMEMs or maximal spanning seeds out of MEMs. A comprehensive benchmarking shows the applicability, strengths, shortcomings and computational requirements of all discussed seeding techniques. Additionally, we report the effects of seed occurrence filters in the context of these techniques. Aside from our novel algorithmic approaches, we analyze hierarchies within fixed-size and variable-size seeding along with a mapping between instances of both seeding strategies. Conclusion Benchmarking shows that our proposed merge-extend strategy for MEM computation outperforms previous extend-purge strategies in the context of PacBio reads. The observed superiority grows with increasing read size and read quality. Further, the presented filters for extracting SMEMs or maximal spanning seeds out of MEMs outperform FMD-index based extension techniques. All code used for benchmarking is available via GitHub at https://github.com/ITBE-Lab/seed-evaluation .

In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincaré inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting. [ABSTRACT FROM AUTHOR]

We consider a control problem associated with a mathematical model of temperature control based on a one-dimensional general type parabolic equation. We define the optimal control function as a minimizer of a quadratic cost functional, prove the existence of a minimizer, and study qualitative properties of control functions. [ABSTRACT FROM AUTHOR]

Minimizers are widely acknowledged cross-linguistically to denote a minimal quantity, extent or degree. With respect to minimizers in Mandarin Chinese, Shyu (Linguistics 54:1355–1395, 2016) claims that their so-called negative polarity is purely syntactically determined and is facilitated by the lian...dou ('including...all') EVEN construction. Within the framework of Dynamic Syntax (Kempson et al., Dynamic syntax: the flow of language understanding, Blackwell, 2001; Cann et al., The dynamics of language, Elsevier, 2005) which allows for interaction between syntactic, semantic and pragmatic information, we demonstrate that the total negation is actually derived from the interaction between syntax, semantics and pragmatics, rather than being determined by purely syntactic means. [ABSTRACT FROM AUTHOR]

We consider a sequence of convex integral functionals Fs : W1,p(Ωs) → ℝ and a sequence of weakly lower semicontinuous and, in general, nonintegral functionals Gs : W1,p(Ωs) → ℝ, where {Ωs} is a sequence of domains in ℝn contained in a bounded domain Ω ⊂ ℝn (n ⩾ 2) p > 1. Along with this, we consider a sequence of closed convex sets Vs = {v ∈ W1,p(Ωs) : Ms(v) ⩽ 0 a.e. in Ωs}, where Ms is a mapping from W1,p(Ωs) to the set of all functions defined on Ωs. We establish conditions under which minimizers and minimum values of the functionals Fs +Gs on the sets Vs converge to a minimizer and the minimum value of a functional on the set V = {v ∈ W1,p(Ω) : M(v) ⩽ 0 a.e. in Ω}, where M is a mapping from W1,p(Ω) to the set of all functions defined on Ω. [ABSTRACT FROM AUTHOR]

In this paper we prove local Hölder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. In the final section, we provide some non-trivial applications of our results.