Miracle-dz/UniFAR-FTUs huggingface dataset:
Representation Learning Using Rank Loss for Robust Neurosurgical Skills Evaluation

Surgical simulators provide hands-on training and learning of the necessary psychomotor skills. Automated skill evaluation of the trainee doctors based on the video of a task being performed by them is an important key step for the optimal utilization of such simulators. However, current skill evaluation techniques require accurate tracking information of the instruments which restricts their applicability to robot assisted surgeries only. In this paper, we propose a novel neural network architecture that can perform skill evaluation using video data alone (and no tracking information). Given the small dataset available for training such a system, the network trained using ℓ2 regression loss easily overfits the training data. We propose a novel rank loss to help learn robust representation, leading to 5% improvement for skill score prediction on the benchmark JIGSAWS dataset. To demonstrate the applicability of our method on non-robotic surgeries, we contribute a new neuro-endoscopic technical skills (NETS) training dataset comprising of 100 short videos of 12 subjects. Our method achieved 27% improvement over the state of the art on the NETS dataset. Project page with source code, and data is available at nets-iitd.github. io/nets-v1.
Polar actions on symmetric spaces of higher rank

We show that polar actions of cohomogeneity 2 on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second‐named author, we are able to prove that polar actions induced by reductive algebraic subgroups in the isometry group of an irreducible Riemannian symmetric space of higher rank are hyperpolar. In particular, this result affirmatively settles the conjecture that polar actions on irreducible compact symmetric spaces of higher rank are hyperpolar.
Limit theorems for the sample autocovariance of a continuous-time moving average process with long memory

We examine the asymptotic behaviour of the sample autocovariance in a continuous-time moving average model with long-range dependence. We show that it is either asymptotically Rosenblatt distributed or stable distributed. This shows that results by Horv\'ath and Kokoszka for discrete-time moving average processes with long memory also hold for continuous-time moving average processes.
Projective geometry of Sasaki–Einstein structures and their compactification

We show that the standard definitions of Sasaki structures have elegant and simplifying interpretations in terms of projective differential geometry. For Sasaki-Einstein structures we use projective geometry to provide a resolution of such structures into geometrically less rigid components; the latter elemental components are separately, complex, orthogonal, and symplectic holonomy reductions of the canonical projective tractor/Cartan connection. This leads to a characterisation of Sasaki-Einstein structures as projective structures with certain unitary holonomy reductions. As an immediate application, this is used to describe the projective compactification of indefinite (suitably) complete non-compact Sasaki-Einstein structures and to prove that the boundary at infinity is a Fefferman conformal manifold that thus fibres over a nondegenerate CR manifold (of hypersurface type). We prove that this CR manifold coincides with the boundary at infinity for the c-projective compactification of the K\"ahler-Einstein manifold that arises, in the usual way, as a leaf space for the defining Killing field of the given Sasaki-Einstein manifold. A procedure for constructing examples is given. The discussion of symplectic holonomy reductions of projective structures leads us moreover to a new and simplifying approach to contact projective geometry. This is of independent interest and is treated in some detail.
Harmonic measure and Riesz transform in uniform and general domains

Abstract Let Ω ⊊ ℝ n + 1 {\Omega\subsetneq{\mathbb{R}}^{n+1}} be open and let μ be some measure supported on ∂ ⁡ Ω {\partial\Omega} such that μ ⁢ ( B ⁢ ( x , r ) ) ≤ C ⁢ r n {\mu(B(x,r))\leq Cr^{n}} for all x ∈ ℝ n + 1 {x\in{\mathbb{R}}^{n+1}} , r > 0 {r>0} . We show that if the harmonic measure in Ω satisfies some scale invariant A ∞ {A_{\infty}} -type conditions with respect to μ, then the n-dimensional Riesz transform ℛ μ ⁢ f ⁢ ( x ) = ∫ x - y | x - y | n + 1 ⁢ f ⁢ ( y ) ⁢ 𝑑 μ ⁢ ( y ) {\mathcal{R}}_{\mu}f(x)=\int\frac{x-y}{|x-y|^{n+1}}f(y)\,d\mu(y) is bounded in L 2 ⁢ ( μ ) {L^{2}(\mu)} . We do not assume any doubling condition on μ. We also consider the particular case when Ω is a bounded uniform domain. To this end, we need first to obtain sharp estimates that relate the harmonic measure and the Green function in this type of domains, which generalize classical results by Jerison and Kenig for the well-known class of NTA domains.
Yokota theory, the invariant trace fields of hyperbolic knots and the Borel regulator map

For a hyperbolic link complement with a triangulation, there are hyperbolicity equations of the triangulation, which guarantee the hyperbolic structure of the link complement. In this paper, we explain that the number of the essential solutions of the equations is equal to or bigger than the extension degree of the invariant trace field of the link. On the other hand, Yokota suggested a potential function of a hyperbolic knot, which gives the hyperbolicity equations and the complex volume of the knot. Applying the fact above to his theory, we explain that the potential function also gives all the values of the Borel regulator map and the complex volumes of the parabolic representations. Furthermore, we explain the maximum value of the imaginary parts of the complex volumes is the volume of the complete hyperbolic structure of the knot complement. Especially, if the number of the essential solutions of the hyperbolicity equations and the extension degree of the invariant trace field are the same, then the evaluation of all essential complex solutions of the hyperbolicity equations to the imaginary part of the potential function is the same with the Borel regulator map. We show these actually happens in the case of the twist knots.
Numerical Approximation of Hyperbolic Systems Containing an Interface

In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides. The numerical solver is based on central methods, like the Rusanov scheme, and does not use the structure of the Riemann Problem. It consists in balancing the effects of the waves that enter the interface. The scheme is well balanced with respect to all the piecewise constant equilibria associated with the interface condition and is able to maintain exactly conservation properties of the interface conditions. A detailed analysis and several numerical tests show the quality of the method. Different applications, including sonic and transsonic flows and a multiphysic model are studied.
Entrance laws at the origin of self-similar Markov processes in high dimensions

In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in R d \mathbb {R}^d , killed upon hitting the origin. Under suitable assumptions, we show the existence of an entrance law and the convergence to this law when the process is started close to the origin. We obtain an explicit description of the process started from the origin as the time reversal of the original self-similar Markov process conditioned to hit the origin.
Positive definiteness and stability of parametric interval matrices

We investigate positive definiteness, Hurwitz stability and Schur stability of parametric interval matrices. We give a verifiable sufficient condition for positive definiteness of parametric interval matrices with non-linear dependencies. We also give several sufficient and necessary conditions for stability of symmetric parametric interval matrices with affine-linear dependencies. The presented results extend the results on positive definiteness and stability of interval matrices. In addition, we provide a formula for the radius of stability of symmetric parametric interval matrices.
An Exploratory Study of MMPI-2-RF Personality and Psychopathology Profiles of Adults with Autism Spectrum Disorder without Intellectual Disability

Objective More empirical research is needed to disentangle the phenotypes of autism spectrum disorder (ASD) and cluster C personality symptomatology (CCPD), as both show similarities in their clinical presentation. We explored personality and psychopathology dimensions as conceptualized in contemporary dimensional taxonomies (i.e., hierarchical taxonomy of psychopathology; HiTOP) in adults with ASD without intellectual disability operationalized by the Minnesota Multiphasic Personality Inventory-2-Restructured Form (MMPI-2-RF). Method Applying secondary analytic processes using clinical data, we cross-examined the MMPI-2-RF profiles of adults with ASD (n = 28) compared to adults with Cluster C personality disorders (CCPD; n = 28) and a control group (n = 28) by conducting nonparametric tests and assessing effect sizes. Results The profiles of the ASD and CCPD groups evidenced to be similar, and both average clinical profiles diverged from the average control group profiles by elevated levels of demoralization, internalizing, and somatization symptomatology. There were small differences between the average profiles of adults with ASD and adults with CCPD. Additional research using dimensional measures of psychopathology could elucidate the dimensional phenotypes of ASD and CCPD. Conclusions Based on the results in this study, the MMPI-2-RF may not meaningfully discriminate between the two clinical presentations, with the exception of various externalizing scales.
Free boundary regularity for a multiphase shape optimization problem

Abstract In this paper we prove a regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman functionals for an energy with variable coefficients. As a consequence, we deduce the complete regularity of solutions of a multiphase shape optimization problem for the first eigenvalue of the Dirichlet Laplacian, up to the boundary of a fixed domain that acts as a geometric inclusion constraint. One of the main ingredients is a new application of the (one-phase) epiperimetric inequality up to the boundary of the constraint. While the framework that leads to this application is valid in every dimension, the epiperimetric inequality is known only in dimension two, thus the restriction on the dimension.
Glycolytic activity in human immune cells: inter-individual variation and functional implications during health and diabetes

An increase in glucose uptake driving aerobic glycolysis is a robust hallmark of immune cell activation. The glycolytic response supports functional alterations of the innate immune cells including the production and release of cytokines. Large inter-individual differences in the magnitude of this cytokine response are known to exist. In addition, the presence of disease is known to impact on immune cell function. Whether variation in metabolic responses of immune cells exist between individuals during health or disease is currently unknown. Here, we explore inter-individual differences in the glycolytic rate of immune cells using lactate production as readout upon activation using a variety of different stimuli. Glycolytic responses are subsequently associated to functional immune cell responses in healthy humans. In addition, we determined the glycolytic rate of immune cells and its association with immune function using patients diagnosed with diabetes mellitus. Based on the relative increase in lactate production after activation, distinct clusters of low, intermediate, and high responders could be identified, illustrating the existence of variation in glycolytic responses in healthy subjects. Interestingly, the production of cytokines mirrored these high-, intermediate-, and low-lactate patterns after pathogenic stimulation. In patients with diabetes mellitus, a reduced correlation was found between lactate and cytokine production, specifically for IL-6. Furthermore, based on the relative increase in lactate production, variability in the glycolytic response was reduced compared to healthy subjects. In conclusion, our results show a specific association between the glycolytic rate and function in human immune cells after stimulation with different pathogens. In addition to demonstrating the existence of glycolytic variability and specificity depending on the type of stimulus, the association between glycolysis and function in innate immune cells is altered during the presence of diabetes.
On subgraphs of $C_{2k}$-free graphs and a problem of K\"uhn and Osthus

Let $c$ denote the largest constant such that every $C_{6}$-free graph $G$ contains a bipartite and $C_4$-free subgraph having $c$ fraction of edges of $G$. Gy\H{o}ri et al. showed that $\frac{3}{8} \le c \le \frac{2}{5}$. We prove that $c=\frac{3}{8}$. More generally, we show that for any $\varepsilon>0$, and any integer $k \ge 2$, there is a $C_{2k}$-free graph $G_1$ which does not contain a bipartite subgraph of girth greater than $2k$ with more than $\left(1-\frac{1}{2^{2k-2}}\right)\frac{2}{2k-1}(1+\varepsilon)$ fraction of the edges of $G_1$. There also exists a $C_{2k}$-free graph $G_2$ which does not contain a bipartite and $C_4$-free subgraph with more than $\left(1-\frac{1}{2^{k-1}}\right)\frac{1}{k-1}(1+\varepsilon)$ fraction of the edges of $G_2$. One of our proofs uses the following statement, which we prove using probabilistic ideas, generalizing a theorem of Erd\H{o}s: For any $\varepsilon>0$, and any integers $a$, $b$, $k \ge 2$, there exists an $a$-uniform hypergraph $H$ of girth greater than $k$ which does not contain any $b$-colorable subhypergraph with more than $\left(1-\frac{1}{b^{a-1}}\right)\left(1+\varepsilon\right)$ fraction of the hyperedges of $H$. We also prove further generalizations of this theorem. In addition, we give a new and very short proof of a result of K\"uhn and Osthus, which states that every bipartite $C_{2k}$-free graph $G$ contains a $C_{4}$-free subgraph with at least $1/(k-1)$ fraction of the edges of $G$. We also answer a question of K\"uhn and Osthus about $C_{2k}$-free graphs obtained by pasting together $C_{2l}$'s (with $k>l\ge3$).
Enumerating limit groups: A Corrigendum

We discuss two possible interpretations of Definition 1.1 from [2]. In [2, Definition 1.1], we made the following definition: Definition 1.1. A coherent group G is effectively coherent if there exists an algorithm that, given a finite subset S as input, outputs a presentation for the subgroup generated by S. A class G of coherent groups is uniformly effectively coherent if there exists an algorithm that, given as input a presentation of a group G ∈ G and a finite set S of elements of G, outputs a presentation for the subgroup of G generated by S. We intended the phrase ‘presentation for the subgroup’ to mean that the presentation has generating set S, so that one knows how the abstract group sits inside G as a subgroup. However, as pointed out to us by Maurice Chiodo, one could interpret our definition to mean that the algorithm merely outputs a presentation for the abstract group 〈S〉, without exhibiting an isomorphism between the group presented and 〈S〉. In order to avoid further confusion, we propose the following definitions to distinguish the two related notions. Definition 1.2. A coherent group G is effectively coherent if there exists an algorithm that, given a finite subset S that generates a subgroup H as input, outputs a presentation 〈S | R〉 for H.
An observation on the uniform preconditioners for the mixed Darcy problem

When solving a multiphysics problem one often decomposes a monolithic system into simpler, frequently single‐physics, subproblems. A comprehensive solution strategy may commonly be attempted, then, by means of combining strategies devised for the constituent subproblems. When decomposing the monolithic problem, however, it may be that requiring a particular scaling for one subproblem enforces an undesired scaling on another. In this manuscript we consider the H(div)‐based mixed formulation of the Darcy problem as a single‐physics subproblem; the hydraulic conductivity, K, is considered intrinsic and not subject to any rescaling. Preconditioners for such porous media flow problems in mixed form are frequently based on H(div) preconditioners rather than the pressure Schur complement. We show that when the hydraulic conductivity, K, is small the pressure Schur complement can also be utilized for H(div)‐based preconditioners. The proposed approach employs an operator preconditioning framework to establish a robust, K‐uniform block preconditioner. The mapping property of the continuous operator is a key component in applying the theoretical framework point of view. As such, a main challenge addressed here is establishing a K‐uniform inf‐sup condition with respect to appropriately weighted Hilbert intersection‐ and sum spaces.
Invariants of links from the generalized Yang-Baxter equation

Enhanced Yang-Baxter operators give rise to invariants of oriented links. We expand the enhancing method to generalized Yang-Baxter operators. At present two examples of generalized Yang-Baxter operators are known and recently three types of variations for one of these were discovered. We present the definition of enhanced generalized YB-operators and show that all known examples of generalized YB-operators can be enhanced to give corresponding invariants of oriented links. Most of these invariants are specializations of the polynomial invariant $P$. Invariants from generalized YB-operators are multiplicative after a normalization.
Refined Chern-Simons theory and Hilbert schemes of points on the plane

Aganagic and Shakirov propose a refinement of the SU(N) Chern-Simons theory for links in three manifolds with S^1-symmetry, such as torus knots in S^3, based on deformation of the S and T matrices, originally found by Kirillov and Cherednik. We relate the large N limit of the S matrix to the Hilbert schemes of points on the affine plane. As an application, we find an explicit formula for the Euler characteristics of the universal sheaf, applied arbitrary Schur functor.
Some Rapidly Converging Series for $\zeta(2n+1)$ from Abstract Operators

The author derives new family of series representations for the values of the Riemann Zeta function $\zeta(s)$ at positive odd integers. For $n\in\mathbb{N}$, each of these series representing $\zeta(2n+1)$ converges remarkably rapidly with its general term having the order estimate: $$O(m^{-2k}\cdot k^{-2n+1})\qquad(k\rightarrow\infty;\quad m=3,4,6). $$ The method is based on the mapping relationships between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, including the mapping relationships between power series and trigonometric series, if each coefficient of a power series is respectively equal to that of a trigonometric series. Thus we obtain a general method to find the sum of the Dirichlet series of integer variables. By defining the Zeta function in an abstract operators form, we have further generalized these results on the whole complex plane.
Infinite Systems of Competing Brownian Particles

Consider a system of infinitely many Brownian particles on the real line. At any moment, these particles can be ranked from the bottom upward. Each particle moves as a Brownian motion with drift and diffusion coefficients depending on its current rank. The gaps between consecutive particles form the (infinite-dimensional) gap process. We find a stationary distribution for the gap process. We also show that if the initial value of the gap process is stochastically larger than this stationary distribution, this process converges back to this distribution as time goes to infinity. This continues the work by Pal and Pitman (2008). Also, this includes infinite systems with asymmetric collisions, similar to the finite ones from Karatzas, Pal and Shkolnikov (2016).
TRANSGENERATIONAL EFFECT OF EARLY CHILDHOOD FAMINE EXPOSURE IN THE COHORT OF OFFSPRING OF LENINGRAD SIEGE SURVIVORS.

Abstract Introduction: Environmental exposure during early life development can affect disease risk in late-life period. There is little data on the transmission of phenotypic features from famine-exposed individuals to the next generations. Objective: The purpose of our study was to investigate the association of parental starvation in the perinatal period and the period of early childhood with the phenotypic features observed in two generations of descendants of Leningrad Siege survivors (DLSS). Design and methods: We examined 54 children and 30 grandchildren of 58 besieged Leningrad residents who suffered from starvation in early childhood and prenatal age during the Second World War. Controls from the population-based national epidemiological ESSE-RF study (n=175) were matched on sex, age and body mass index (BMI). Anthropometry, blood pressure (BP) measurement, and blood tests were performed for both groups. Sociodemographic and lifestyle information was collected via questionnaires. Phenotypes of controls and descendants (combined and children and grandchildren separately) were compared, taking into account multiple testing. Results: Comparison of two generations descendants with corresponding control groups revealed significantly higher creatinine level and lower glomerular filtration rate (GFR), both in meta-analysis and in both generations independently. The mean values of GFR for all groups were detected within the normal range. Additionally, independent of the creatinine level, differences in the eating pattern were detected: insufficient fish consumption and excessive red meat consumption were significantly more frequent in the children of the Leningrad siege survivors compared with controls. BP and blood lipids did not differ between the groups. Conclusions: Ancestral famine exposure in the prenatal period and early childhood may contribute to a decrease of in kidney filtration capacity and altered eating pattern in at least two generations of besieged Leningrad offspring.
On uniform distribution for invariant extensions of the linear Lebesgue measure

The concept of uniform distribution in $[0,1]$ is extended for a certain strictly separated maximal (in the sense of cardinality) family $(\lambda_t)_{t \in [0,1]}$ of invariant extensions of the linear Lebesgue measure $\lambda$ in $[0.1]$, and it is shown that the $\lambda_t^{\infty}$ measure of the set of all $\lambda_t$-uniformly distributed sequences is equal to $1$, where $\lambda_t^{\infty}$ denotes the infinite power of the measure $\lambda_t$. This is an analogue of Hlawka's (1956) theorem for $\lambda_t$-uniformly distributed sequences. An analogy of Weyl's (1916) theorem is obtained in similar manner.
Dual-function artificial molecular motors performing rotation and photoluminescence

Molecular machines have caused one of the greatest paradigm shifts in chemistry, and by powering artificial mechanical molecular systems and enabling autonomous motion, they are expected to be at the heart of exciting new technologies. One of the biggest challenges that still needs to be addressed is designing the involved molecules to combine different orthogonally controllable functions. Here, we present a prototype of artificial molecular motors exhibiting the dual function of rotary motion and photoluminescence. Both properties are controlled by light of different wavelengths or by exploiting motors’ outstanding two-photon absorption properties using low-intensity near-infrared light. This provides a noninvasive way to both locate and operate these motors in situ, essential for the application of molecular machines in complex (bio)environments.