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Abstract: Background. Intraspinal synovial cysts of vertebral facet joints are uncommon cause of radicular pain as well as neurological deficits. They can be managed both conservatively and surgically.Case report. A 77-year old polymorbid patient presented with bilateral low back pain which worsened during the course of time and did not respond to the conservative treatment. A diagnosis of intraspinal synovial cyst was made using the magnetic resonance imaging (MRI). Percutaneous computed tomography (CT) guided injection with installation of local anesthetic together with corticosteroid and rupture of the cyst was successfully used. A month after the procedure his pain improved, the usage of analgesics diminished and his over-all quality of life improved.Conclusions. Percutaneous CT guided lumbar synovial cyst treatment is safe and reliable alternative to the surgical treatment in polymorbid patients with radiculopathy who are not able to tolerate general anesthesia and operation.
Keywords: ciste, intraspinalne sinovialne ciste, bolečina, zdravljenje, radiologija
Published in DiRROS: 11.04.2024; Views: 68; Downloads: 34
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Keywords: onkologija, rak (medicina), ledvice, karcinom, diagnostika
Published in DiRROS: 10.04.2024; Views: 68; Downloads: 13
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Abstract: We show that if $\Omega$ is an $m$-convex domain in $\mathbb{R}^n$ for some $2 \le m < n$ whose boundary $b\Omega$ has a tubular neighbourhood of positive radius and is not $m$-flat near infinity, then $\Omega$ does not contain any immersed parabolic minimal submanifolds of dimension $\ge m$. In particular, if $M$ is a properly embedded non-flat minimal hypersurface in $\mathbb{R}^n$ with a tubular neighbourhood of positive radius, then every immersed parabolic hypersurface in $\mathbb{R}^n$ intersects $M$. In dimension $n=3$, this holds if $M$ has bounded Gaussian curvature function. We also introduce the class of weakly hyperbolic domains $\Omega$ in $\mathbb{R}^n$, characterised by the property that every conformal harmonic map $\mathbb{C} \to \Omega$ is constant, and we elucidate their relationship with hyperbolic domains, and domains without parabolic minimal surfaces.
Keywords: minimal surfaces, m-plurisubharmonic functions, hyperbolic domain
Published in DiRROS: 10.04.2024; Views: 67; Downloads: 29
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Abstract: If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$ and has been already investigated. In this paper a variety of mutual-visibility problems is introduced based on which natural pairs of vertices are required to be $X$-visible. This yields the total, the dual, and the outer mutual-visibility numbers. We first show that these graph invariants are related to each other and to the classical mutual-visibility number, and then we prove that the three newly introduced mutual-visibility problems are computationally difficult. According to this result, we compute or bound their values for several graphs classes that include for instance grid graphs and tori. We conclude the study by presenting some inter-comparison between the values of such parameters, which is based on the computations we made for some specific families.
Keywords: mutual-visibility, total mutual-visibility, dual mutual-visibility number, outer mutual-visibility, grid graphs, torus graphs, computational complexity
Published in DiRROS: 10.04.2024; Views: 71; Downloads: 33
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Abstract: We consider persistent homology obtained by applying homology to the open Rips filtration of a compact metric space $(X, d)$. We show that each decrease in zero-dimensional persistence and each increase in one-dimensional persistence is induced by local minima of the distance function $d$ When $d$ attains local minimum at only finitely many pairs of points, we prove that each above mentioned change in persistence is induced by a specific critical edge in Rips complexes, which represents a local minimum of $d$. We use this fact to develop a theory (including interpretation) of critical edges of persistence. The obtained results include upper bounds for the rank of one-dimensional persistence and a corresponding reconstruction result. Of potential computational interest is a simple geometric criterion recognizing local minima of $d$ that induce a change in persistence. We conclude with a proof that each locally isolated minimum of $d$ can be detected through persistent homology with selective Rips complexes. The results of this paper offer the first interpretation of critical scales of persistent homology (obtained via Rips complexes) for general compact metric spaces.
Keywords: persistent homology, Rips complex, critical simplex, reconstruction result
Published in DiRROS: 10.04.2024; Views: 52; Downloads: 23
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