arXiv subjects

Antti Kemppainen

Publications and source records attributed to Antti Kemppainen.

10 recordsLinked to original sources

arXiv2026

Landmark-free Assessment of Lower-limb Alignment with Implicit Neural Shape Functions from Knee Radiographs

Radiographic assessment of lower-limb alignment (LLA) is important for predicting joint health and surgical outcomes in total knee arthroplasty. Traditional measurement methods are manual and time-consuming, while recent machine learning approaches typically rely on locating a fixed set of anatomical landmarks. This dependence limits flexibility and may require re-annotation when clinical definitions change. To address this, we propose an automated workflow using Implicit Neural Shape Functions (INSF). Rather than relying on explicit landmark coordinates, we encode the anatomy into a compact latent space and regress clinical alignment measurements directly from these latent codes. This architecture allows for rapid extendability to new tasks without altering the backbone representation. We trained our method on an internal dataset of 566 knee radiographs, each annotated with the outline of the femur and tibia. We evaluated it on both an internal test dataset of 50 patients and a separate external set of 402 preoperative cases from the MRKR dataset. Manual clinical measurements are available for these data, and the MRKR measurements will be made publicly accessible. Performance was comparable to state-of-the-art landmark-based methods and manual agreement, while offering a flexible shape representation that can be extended to additional measurement tasks.

cs.CV↗

arXiv2023

Energy correlations in the critical Ising model on a torus

We compute rigorously the scaling limit of multi-point energy correlations in the critical Ising model on a torus. For the one-point function, averaged between horizontal and vertical edges of the square lattice, this result has been known since the 1969 work of Ferdinand and Fischer. We propose an alternative proof, in a slightly greater generality, via a new exact formula in terms of determinants of discrete Laplacians. We also compute the main term of the asymptotics of the difference $\mathbb{E}(ε_{V}-ε_{H})$ of the energy density on a vertical and a horizontal edge, which is of order of $δ^{2}$, where $δ$ is the mesh size. The observable $ε_{V}-ε_{H}$ has been identified by Kadanoff and Ceva as (a component of) the stress-energy tensor. We then apply the discrete complex analysis methods of Smirnov and Hongler to compute the multi-point correlations. The fermionic observables are only periodic with doubled periods; by anti-symmetrization, this leads to contributions from four "sectors". The main new challenge arises in the doubly periodic sector, due to the existence of non-zero constant (discrete) analytic functions. We show that some additional input, namely the scaling limit of the one-point function and of relative contribution of sectors to the partition function, is sufficient to overcome this difficulty and successfully compute all correlations.

math-ph↗

arXiv2019

Conformal invariance in random cluster models. II. Full scaling limit as a branching SLE

In the second article of this series, we establish the convergence of the loop ensemble of interfaces in the random cluster Ising model to a conformal loop ensemble (CLE) --- thus completely describing the scaling limit of the model in terms of the random geometry of interfaces. The central tool of the present article is the convergence of an exploration tree of the discrete loop ensemble to a branching SLE$(16/3,-2/3)$. Such branching version of the Schramm's SLE not only enjoys the locality property, but also arises logically from the Ising model observables.

math-ph↗

arXiv2019

Conformal invariance of boundary touching loops of FK Ising model

In this article we show the convergence of a loop ensemble of interfaces in the FK Ising model at criticality, as the lattice mesh tends to zero, to a unique conformally invariant scaling limit. The discrete loop ensemble is described by a canonical tree glued from the interfaces, which then is shown to converge to a tree of branching SLEs. The loop ensemble contains unboundedly many loops and hence our result describes the joint law of infinitely many loops in terms of SLE type processes, and the result gives the full scaling limit of the FK Ising model in the sense of random geometry of the interfaces. Some other results in this article are convergence of the exploration process of the loop ensemble (or the branch of the exploration tree) to SLE$(κ,κ-6)$, $κ=16/3$, and convergence of a generalization of this process for $4$ marked points to SLE$[κ,Z]$, $κ=16/3$, where $Z$ refers to a partition function. The latter SLE process is a process that can't be written as a SLE$(κ,ρ_1,ρ_2,\ldots)$ process, which are the most commonly considered generalizations of SLEs.

math-ph↗

arXiv2017

Configurations of FK Ising interfaces and hypergeometric SLE

In this paper, we show that the interfaces in FK Ising model in any domain with 4 marked boundary points and wired--free--wired--free boundary conditions conditioned on a specific internal arc configuration of interfaces converge in the scaling limit to hypergeometric SLE (hSLE). The arc configuration consists of a pair of interfaces and the scaling limit of their joint law can be described by an algorithm to sample the pair from a hSLE curve and a chordal SLE (in a random domain defined by the hSLE).

math-ph↗

arXiv2015

Random curves, scaling limits and Loewner evolutions

In this paper, we provide a framework of estimates for describing 2D scaling limits by Schramm's SLE curves. In particular, we show that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical mechanics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces. Interestingly, our proofs indicate that existence of a nondegenerate observable with a conformally-invariant scaling limit seems sufficient to deduce the required condition. Our paper serves as an important step in establishing the convergence of Ising and FK Ising interfaces to SLE curves, moreover, the setup is adapted to branching interface trees, conjecturally describing the full interface picture by a collection of branching SLEs.

math-ph↗

arXiv2014

The nested simple conformal loop ensembles in the Riemann sphere

Simple conformal loop ensembles (CLE) are a class of random collection of simple non-intersecting loops that are of particular interest in the study of conformally invariant systems. Among other things related to these CLEs, we prove the invariance in distribution of their nested "full-plane" versions under the inversion $z \mapsto 1/z$.

math.PR↗

arXiv2013

Convergence of Ising interfaces to Schramm's SLE curves

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE curves with parameter $κ=3$ and $κ=16/3$ respectively.

math-ph↗

arXiv2009

Stationarity of SLE

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using this approach. Some example calculations are presented.

math-ph↗

arXiv2006

SLE local martingales, reversibility and duality

We study SLE reversibility and duality using the Virasoro structure of the space of local martingales. For both problems we formulate a setup where the questions boil down to comparing two processes at a stopping time. We state algebraic results showing that local martingales for the processes have enough in common. When one has in addition integrability, the method gives reversibility and duality for any polynomial expected value.

math-ph↗