Miracle-dz/UniFAR-FTUs huggingface dataset:
Case report: Surgical resection of a retro-hepatic leiomyosarcoma involving atrial reconstruction, cardiopulmonary bypass, ex vivo tumor resection, and liver re-implantation

Introduction Leiomyosarcomas (LMS) involving the inferior vena cava (IVC) is a clinically rare entity, accounting for approximately 0.5% of all adult sarcomas. Case presentation A 67-year-old male presented to the emergency department with mild back and lower abdominal pain. During the workup, a computed tomography scan without contrast showed an area of decreased attenuation within the liver adjacent to the intrahepatic IVC. Magnetic resonance imaging confirmed the involvement of the retro-hepatic IVC; biopsy confirmed the diagnosis of LMS. Given the location of the involvement of the retro-hepatic IVC, liver explantation was deemed necessary for adequate tumor resection. The superior extension of the tumor toward the heart necessitated Cardio-Pulmonary (CPB). The patient successfully underwent a complex surgical procedure involving liver explantation with ex vivo back-table resection of the retro-hepatic LMS, replacement of the retro-hepatic vena cava with a ringed Gore-Tex graft, liver re-implantation, and hepatic vein-atrial reconstruction under cardiopulmonary bypass. There were no intraoperative or post-op complications. Discussion The role of vascular reconstruction of the IVC varies depending on the level and extent of the tumor, with options ranging from primary repair, ligation, or reconstruction dictated. Surgical resection with negative margins remains the treatment of choice due to the lack of efficacy of adjuvant therapies. Importantly, liver explantation offers a chance for complete surgical resection and reconstruction. Similarly, the complex nature of the tumor necessitated a pioneering approach involving direct hepato-atrial venous anastomosis. Conclusion To the best of our knowledge, this is the first reported case in which the hepatic veins were anastomosed directly to the right atrium while also replacing the native vena cava with a separate graft.
Editorial: Temporal lobe dysfunction in neuropsychiatric disorder

tonic-clonic seizure (FBTCS), using four basal forebrain subregions to examine the resting-state FC (rsFC). Regardless of FBTCS status, the TLE patients had reduced rsFC of BF subregions the frontal and lobes. Decreased rsFC of Ch1-3 with bilateral and left cerebellum posterior lobe and Ch4 with bilateral amygdala was associated with FBTCS.
Power maps in algebra and topology

Given any twisting cochain t:C -->A, where C is a connected, coaugmented chain coalgebra and A is an augmented chain algebra over an arbitrary PID R, we construct a twisted extension of chain complexes A --> H(t) --> C. We show that both the well-known Hochschild complex of an associative algebra and the coHochschild complex of a coassociative coalgebra are special cases of H(t), which we therefore call the Hochschild complex of t. We explore the extent of the naturality of the Hochschild complex construction and apply the results of this exploration to determining conditions under which H(t) admits multiplicative or comultiplicative structure. In particular, we show that the Hochschild complex on a chain Hopf algebra always admits a natural comultiplication. Furthermore, when A is a chain Hopf algebra, we determine conditions under which H(t) admits an rth-power map extending the usual rth-power map on A and lifting the identity on C. As special cases, we obtain that both the Hochschild complex of any cocommutative Hopf algebra and the coHochschild complex of the normalized chain complex of a double suspension admit power maps. We show moreover that if K is a double suspension, then the power map on the coHochschild complex of the normalized chain complex of K is a model of the topological power map on the space of free loops on the realization of K, illustrating the topological relevance of our algebraic construction.
Clustering patterns of metabolic syndrome: A cross-sectional study in children and adolescents in Kyiv

Objective The aim: to identify subgroups by cluster analysis according parameters: original homeostatic model of insulin resistance (HOMA-1 IR), updated computer model of insulin resistance (HOMA-2 IR), β-cell function (%B) and insulin sensitivity (%S) for the prognosis of different variants of metabolic syndrome in children for more individualized treatment selection. Patients and methods The observational cross-sectional study on 75 children aged from 10 to 17 with metabolic syndrome according to the International Diabetes Federation criteria was conducted at the Cardiology Department of Children's Clinical Hospital No.6 in Kyiv. HOMA-1 IR was calculated as follows: fasting insulin (µIU/ml) × fasting glucose (mmol/L)/22.5. HOMA-2 IR with %B and %S were calculated according to the computer model in [http://www.dtu. ox.ac. uk]. All biochemical analysis were carried out using Cobas 6000 analyzer and Roche Diagnostics (Switzerland). The statistical analysis was performed using STATISTICA 7.0 and Easy R. The hierarchical method Ward was used for cluster analysis according the parameters: HOMA-1 IR, HOMA-2 IR, %B and %S. Results Four clusters were identified from the dendrogram, which could predict four variants in the course of metabolic syndrome such that children in cluster 1 would have the worst values of the studied parameters and those in cluster 4 – the best. It was found that HOMA-1 IR was much higher in cluster 1 (6.32 ± 0.66) than in cluster 4 (2.19 ± 0.13). HOMA-2 IR was also much higher in cluster 1 (3.80 ± 0.34) than in cluster 4 (1.31 ± 0.06). By the analysis of variance using Scheffe's multiple comparison method, a statistically significant difference was obtained between the laboratory parameters among the subgroups: HOMA-1 IR (p < 0,001), glucose (p < 0.001), insulin (p < 0,001), HOMA-2 IR (p < 0.001), %B (p < 0.001), %S (p < 0.001), TG (p = 0.005) and VLDL-C (p = 0.002). Conclusions A cluster analysis revealed that the first two subgroups of children had the worst insulin resistance and lipid profile parameters. It was found positive correlation between HOMA-1 IR, HOMA-2 IR, %B and %S with lipid metabolism parameters TG and VLDL-C and negative correlation between %B and HDL-C in children with metabolic syndrome (MetS). The risk of getting a high TG result in the blood analysis in children with MetS was significantly dependent with the HOMA-2 IR >2.26.
An affine Orlicz Polya-Szego principle

The author established the affine Orlicz Polya-Szego principle for log-concave functions and conjectured that the principle can be extended to the general Orlicz Sobolev functions. In this paper, we confirm this conjecture completely. An affine Orlicz Polya-Szego principle, which includes all the previous affine Polya-Szego principles as special cases, is formulated and proved. As a consequence, an Orlicz-Petty projection inequality for star bodies is established.
HOW EXPLICIT KNOWLEDGE AFFECTS ONLINE L2 PROCESSING

Form-focused instruction studies generally report larger gains for explicit types of instruction over implicit types on measures of controlled production. Studies that used online processing measures—which do not readily allow for the application of explicit knowledge—however, suggest that this advantage occurs primarily when the target structure is similar in the first language (L1) and the second language (L2). This study investigated how explicit knowledge of a structure that does not exist in the L1 affects the initial stage of adult L2 acquisition. Fifty-one Dutch L1 speakers received a short auditory exposure (instruction) to a new language that included differential object marking (DOM), in which animate but not inanimate direct objects are preceded by a preposition. For 26 learners, the instruction was complemented by a brief rule explanation. Afterward, learners’ online processing and explicit knowledge of DOM were measured by means of eye-tracking (visual world paradigm) and oral grammaticality judgments. Results show that metalinguistic information promoted learners’ performance on the grammaticality judgment task. Although differences between the groups were also found on the eye-tracking measure, learners were not able to use DOM to predict the following object.
Double Groupoids, Orbifolds, and the Symplectic Category

Motivated by an attempt to better understand the notion of a symplectic stack, we introduce the notion of a \emph{symplectic hopfoid}, which should be thought of as the analog of a groupoid in the so-called symplectic category. After reviewing some foundational material on canonical relations and this category, we show that symplectic hopfoids provide a characterization of symplectic double groupoids in these terms. Then, we show how such structures may be used to produce examples of symplectic orbifolds, and conjecture that all symplectic orbifolds arise via a similar construction. The symplectic structures on the orbifolds produced arise naturally from the use of canonical relations.The characterization of symplectic double groupoids mentioned above is made possible by an observation which provides various ways of realizing the core of a symplectic double groupoid as a symplectic quotient of the total space, and includes as a special case a result of Zakrzewski concerning Hopf algebra objects in the symplectic category. This point of view also leads to a new proof that the core of a symplectic double groupoid itself inherits the structure of a symplectic groupoid. Similar constructions work more generally for any double Lie groupoid---producing what we call a \emph{Lie hopfoid}---and we describe the sense in which a version of the ``cotangent functor'' relates such hopfoid structures.
Noncommutative martingale concentration inequalities

We establish an Azuma type inequality under a Lipshitz condition for martingales in the framework of noncommutative probability spaces and apply it to deduce a noncommutative Heoffding inequality as well as a noncommutative McDiarmid type inequality. We also provide a noncommutative Azuma inequality for noncommutative supermartingales in which instead of a fixed upper bound for the variance we assume that the variance is bounded above by a linear function of variables. We then employ it to deduce a noncommutative Bernstein inequality and an inequality involving $L_p$-norm of the sum of a martingale difference.
Spectral flow for skew-adjoint Fredholm operators

An analytic definition of a $\mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through $0$ along the path. The $\mathbb{Z}_2$-valued spectral flow is shown to satisfy a concatenation property and homotopy invariance, and it provides an isomorphism on the fundamental group of the real skew-adjoint Fredholm operators. Moreover, it is connected to a $\mathbb{Z}_2$-index pairing for suitable paths. Applications concern the zero energy bound states at defects in a Majorana chain and a spectral flow interpretation for the $\mathbb{Z}_2$-polarization in these models.
Edge Computing Based Machine Learning Mobile Malware Detection

Because network infrastructure and bandwidth cannot keep up with the increasing demands, edge computing has sprung up to reorganize the cloud computing paradigm. As an application of edge computing, mobile malware detection requires signiﬁcant resources that are unavailable to individual devices. The immediacy of malware detection is highly pertinent, as malicious software may already be in operation. In addition, the dispersion of mobile devices and massive simultaneous traﬃc make the oﬄoading this work to remote data centers infeasible. In our study, we implement a typical edge node to perform Android malware detection. In our study, we collect an exceptional amount of mobile malware and benign samples, and demonstrate the ability of edge computing nodes to provide typical security functions for edge devices. We also show the ability to scale the operation for increasing data volumes.
Contractible stability spaces and faithful braid group actions

We prove that any `finite-type' component of a stability space of a triangulated category is contractible. The motivating example of such a component is the stability space of the Calabi--Yau-$N$ category $\mathcal{D}(\Gamma_N Q)$ associated to an ADE Dynkin quiver. In addition to showing that this is contractible we prove that the braid group $\operatorname{Br}(Q)$ acts freely upon it by spherical twists, in particular that the spherical twist group $\operatorname{Br}(\Gamma_N Q)$ is isomorphic to $\operatorname{Br}(Q)$. This generalises Brav-Thomas' result for the $N=2$ case. Other classes of triangulated categories with finite-type components in their stability spaces include locally-finite triangulated categories with finite rank Grothendieck group and discrete derived categories of finite global dimension.
Module Pseudo-amenability of Banach algebras

The notions of module pseudo-amenable and module pseudo-contractible Banach algebras are introduced. For a Banach algebra with bounded approximate identity, module pseudo-amenability and module approximate amenability are the same properties. It is given a complete characterization of module pseudo-amenability for a Banach algebra. For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, necessary and sufficient conditions are obtained for the $\ell^1(S)$ and its second dual to be $\ell^1(E)$-module pseudo-amenable.
Tangle Floer homology and cobordisms between tangles

We introduce a generalization of oriented tangles, which are still called tangles, so that they are in one‐to‐one correspondence with the sutured manifolds. We define cobordisms between sutured manifolds (tangles) by generalizing cobordisms between oriented tangles. For every commutative algebra A over Z/2Z , we define A-Tangles to be the category consisting of A ‐tangles, which are balanced tangles with A ‐colorings of the tangle strands and fixed Spinc structures, and A ‐cobordisms as morphisms. An A ‐cobordism is a cobordism with a compatible A ‐coloring and an isotropic set of Spinc structures. Associated with every A ‐module M we construct a functor HFM:A-Tangles⟶A-Modules,called the tangle Floer homology functor, where A-Modules denotes the category of A ‐modules and A ‐homomorphisms between them. Moreover, for any A ‐tangle T the A ‐module HFM(T) is the extension of sutured Floer homology defined in an earlier work of the authors.
Relativistically exact eikonal equation for optical fibers with application to adiabatically deforming ring interferometers

We derive the relativistically exact Eikonal equation for ring interferometers undergoing deformations. For ring interferometers that undergo slow deformation we describe the two leading terms in the adiabatic expansion of the phase shift. The leading term is independent of the refraction index $n$ and is given by a line integral generalizing results going back to Sagnac \cite{sagnac1913,wang2004,Ori} for non-deforming interferometers to all orders in {$\beta=|\mathbf{v}|/c$}. In the non-relativistic limit {this term} is $O(\beta)$. The next term in the adiabaticity has the form of a double integral, it is of order $\beta^0$ and depends on the refractive index $n$. It accounts for non-reciprocity due to changing circumstances in the fiber. The adiabatic correction is often comparable to the Sagnac term. In particular, this is the case in Fizeau's interferometer. Besides providing a mathematical framework that puts all ring interferometers under a single umbrella, our results generalize and strengthen results of \cite{Ori, shupe} to fibers with chromatic dispersion.
Mathematik in den Naturwissenschaften Leipzig Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler–Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière’s regularity theory and Riesz potential theory.
On uniqueness of solutions to martingale problems — counterexamples and sufficient criteria

The dynamics of a Markov process are often specified by its infinitesimal generator or, equivalently, its symbol. This paper contains examples of analytic symbols which do not determine the law of the corresponding Markov process uniquely. These examples also show that the law of a polynomial process is not necessarily determined by its generator. On the other hand, we show that a combination of smoothness of the symbol and ellipticity warrants uniqueness in law. The proof of this result is based on proving stability of univariate marginals relative to some properly chosen distance.
A model for the multiwavelength radiation from tidal disruption event Swift J1644+57

Gamma-ray observations of a stellar tidal disruption event (TDE) detected by the Swift satellite and follow up observations in radio, mm, infrared and x-ray bands have provided a rich data set to study accretion onto massive blackholes, production of relativistic jets and their interaction with the surrounding medium. The radio and x-ray data for TDE Swift J1644+57 provide a conflicting picture regarding the energy in relativistic jet produced in this event: x-ray data suggest jet energy declining with time as t^{-5/3} whereas the nearly flat lightcurves in radio and mm bands lasting for about 100 days have been interpreted as evidence for the total energy output increasing with time. We show in this work that flat lightcurves do not require addition of energy to decelerating external shock (which produced radio and mm emission via synchrotron process), instead the flat behavior is due to inverse-Compton cooling of electrons by x-ray photons streaming through the external shock; the higher x-ray flux at earlier times cools electrons more rapidly thereby reducing the emergent synchrotron flux, and this effect weakens as the x-ray flux declines with time.
Classification of scaling limits of uniform quadrangulations with a boundary

We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe different limiting metric spaces. Among well-known objects like the Brownian plane or the infinite continuum random tree, we construct two new one-parameter families of metric spaces that appear as scaling limits: the Brownian half-plane with skewness parameter $\theta$ and the infinite-volume Brownian disk of perimeter $\sigma$. We also obtain various coupling and limit results clarifying the relation between these objects.
Slowly Decaying Waves on Spherically Symmetric Spacetimes and an Instability of Ultracompact Neutron Stars

We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves are treated as a model for nonlinear perturbations, this slow decay is highly suggestive of nonlinear instability. We also prove that, in a large class of asymptotically flat, spherically symmetric spacetimes, logarithmic decay actually holds as a uniform upper bound. In the presence of stable trapping, this result is therefore the best one can obtain. In addition, we provide an application of these results to ultracompact neutron stars, suggesting that all stars with r < 3M might be unstable.
Galois module structure and Jacobians of Fermat curves

The class‐invariant homomorphism allows one to measure the Galois module structure of extensions obtained by dividing points on abelian varieties. In this paper, we consider the case when the abelian variety is the Jacobian of a Fermat curve. We give examples of torsion points whose associated Galois structure is trivial, as well as points of infinite order whose associated Galois structure is non‐trivial.
Grid diagrams of Lorenz links

In paper "A new twist on Lorenz links" (Journal of Topology 2(2009), 227-248) Joan Birman and Ilya Kofman prove the coincidence of the class of Lorenz links and the class of twisted links. The proof in that work is algebraic. We will identify this class in terms of grid diagrams and provide a transparent geometric argument for Birman-Kofman's result.
Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process

Using the determinantal formula of Biane, Bougerol, and O’Connell, we give multitime joint probability densities to the noncolliding Brownian motion with drift, where the number of particles is finite. We study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well-ordered with a scale σ. We show that, at each time t > 0, the single-time probability density of particle system is exactly transformed to the biorthogonal Stieltjes-Wigert matrix model in the Chern-Simons theory introduced by Dolivet and Tierz. Here, one-parameter extensions (θ-extensions) of the Stieltjes-Wigert polynomials, which are themselves q-extensions of the Hermite polynomials, play an essential role. The two parameters a and σ of the process combined with time t are mapped to the parameters q and θ of the biorthogonal polynomials. By the transformation of normalization factor of our probability density, the partition function of the Chern-Simons matrix.
Heat equation and Poisson equation in matrix geometry

In this paper, we study the Poisson equation and heat equation in a model matrix geometry $M_n$. Our main results are about the Poisson equation and global behavior of the heat equation on $M_n$. We can show that if $c_0$ is the initial positive definite matrix in $M_n$, then $c(t)$ exists for all time and is positive definite too. We can also show the entropy stability of the solutions to the heat equation.
A duality map for the quantum symplectic double

This paper is a continuation of the author's work with Kim (arXiv:1509.01567), which provided a natural $q$-deformation of Fock and Goncharov's canonical basis for the coordinate ring of a cluster variety associated to a punctured surface. Here we consider a cluster variety called the symplectic double, defined for an oriented disk with finitely many marked points on its boundary. We construct a natural map from the tropical integral points of the symplectic double into its quantized algebra of rational functions. Using this construction, we extend the results of arXiv:1509.01567 to the case of a disk with marked points.
Exact Controllability of the Distributed System Governed by the Wave Equation with Memory

We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to the null state in finite time, the absolute value of the distributed control function being bounded. In this case the memory kernel is a linear combination of exponentials.