arXiv subjects

Tanran Zhang

Publications and source records attributed to Tanran Zhang.

9 recordsLinked to original sources

arXiv2026

AQP4 Regulates Gap-Dominated Glymphatic Clearance through Dynamic Gliovascular Coupling

Aquaporin-4 (AQP4) is enriched at perivascular astrocytic endfeet, and impaired AQP4 function or localization is associated with reduced glymphatic transport. However, mechanical models suggest that pressure-driven exchange across the gliovascular interface occurs predominantly through inter-endfoot gaps rather than directly through the AQP4-rich membrane. How AQP4 regulates clearance in such a gap-dominated system remains unclear. We develop a reduced arterial PVS-ECS-venous PVS model coupling vascular deformation, AQP4-mediated endfoot water exchange, dynamic inter-endfoot gap regulation, and tracer transport. Cardiac-like oscillations generate strong bidirectional exchange but weak net clearance, whereas asymmetric vasodilation enhances directional transport by suppressing recovery-phase backflow. Dynamic gap regulation provides additional hydraulic rectification. Although gap-mediated flux is much larger than direct AQP4-mediated flux, PVS-facing AQP4 substantially affects clearance by altering the pressure--volume balance and hence the driving force for the dominant gap pathway. Reducing PVS-facing AQP4 permeability, or redistributing AQP4 away from the PVS-facing membrane at fixed total conductance, reduces cumulative venous output by about 40\%. Aging-like changes in vascular motion, PVS mechanical coupling, and perivascular AQP4 enrichment further compound this impairment. These results suggest that AQP4 regulates gap-dominated glymphatic clearance through dynamic hydraulic coupling at the gliovascular interface.

physics.med-ph↗

arXiv2022

Conformally invariant complete metrics

For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize the completeness of the modulus metric $μ_G$ in terms of a potential-theoretic thickness condition of $\partial G\,,$ Martio's $M$-condition. Next, we prove that $\partial G$ is uniformly perfect if and only if $μ_G$ admits a minorant in terms of a Möbius invariant metric. Several applications to quasiconformal maps are given.

math.CV↗

arXiv2017

On the hyperbolic distance of $n$-times punctured spheres

The length of the shortest closed geodesic in a hyperbolic surface $X$ is called the systole of $X.$ When $X$ is an $n$-times punctured sphere $\hat{ \mathbb{C}} \setminus A$ where $A \subset \hat{\mathbb{C}}$ is a finite set of cardinality $n\ge4,$ we define a quantity $Q(A)$ in terms of cross ratios of quadruples in $A$ so that $Q(A)$ is quantitatively comparable with the systole of $X.$ We next propose a method to construct a distance function $d_X$ on a punctured sphere $X$ which is Lipschitz equivalent to the hyperbolic distance $h_X$ on $X.$ In particular, when the construction is based on a modified quasihyperbolic metric, $d_X$ is Lipschitz equivalent to $h_X$ with Lipschitz constant depending only on $Q(A).$

math.CV↗

arXiv2017

Construction of nearly hyperbolic distance on punctured spheres

We define a distance function on the bordered punctured disk $0<|z|\le 1/e$ in the complex plane, which is comparable with the hyperbolic distance of the punctured unit disk $0<|z|<1.$ As an application, we will construct a distance function on an $n$-times punctured sphere which is comparable with the hyperbolic distance. We also propose a comparable quantity which is not necessarily a distance function on the punctured sphere but easier to compute.

math.CV↗

arXiv2014

Priority-Aware Private Matching Schemes for Proximity-Based Mobile Social Networks

The rapid developments of mobile devices and online social networks have resulted in increasing attention to Mobile Social Networking (MSN). The explosive growth of mobile-connected and location-aware devices makes it possible and meaningful to do the Proximity-based Mobile Social Networks (PMSNs). Users can discover and make new social interactions easily with physical-proximate mobile users through WiFi/Bluetooth interfaces embedded in their smartphones. However, users enjoy these conveniences at the cost of their growing privacy concerns. To address this problem, we propose a suit of priority-aware private matching schemes to privately match the similarity with potential friends in the vicinity. Unlike most existing work, our proposed priority-aware matching scheme (P-match) achieves the privacy goal by combining the commutative encryption function and the Tanimoto similarity coefficient which considers both the number of common attributes between users as well as the corresponding priorities on each common attribute. Further, based on the newly constructed similarity function which takes the ratio of attributes matched over all the input set into consideration, we design an enhanced version to deal with some potential attacks such as unlimitedly inputting the attribute set on either the initiator side or the responder side, etc. Finally, our proposed E-match avoids the heavy cryptographic operations and improves the system performance significantly by employing a novel use of the Bloom filter. The security and communication/computation overhead of our schemes are thoroughly analyzed and evaluated via detailed simulations and implementation.

cs.CR↗

arXiv2014

Uniformisation of a once-punctured annulus

The universal cover or the covering group of a hyperbolic Riemann surface $X$ is important but hard to express explicitly. It can be, however, detected by the uniformisation and a suitable description of $X$. Beardon proposed five different ways to describe twice-punctured disks using fundamental domain, hyperbolic length, collar and extremal length in 2012. We parameterize a once-punctured annulus $A$ in terms of five parameter pairs and give explicit formulas about the hyperbolic structure and the complex structure of $A$. Several degenerating cases are also treated.

math.CV↗

arXiv2013

Variants of Ahlfors' lemma and properties of the logarithmic potentials

As a special class of conformal metrics with negative curvatures, SK-metrics play a crucial role in metric spaces. This paper concerns the variants of Ahlfors' lemma in an SK-metric space and gives a higher order derivative formula for the logarithmic potential function, which can be applied for the estimates near the singularity of a conformal metric with negative curvatures.

math.CV↗

arXiv2013

A note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularities

The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity for at most second order derivatives was described by Kraus and Roth in one of their papers in 2008. Our work improves one estimate of theirs and shows the estimate for higher order derivatives near an isolated singularity by means of potential theory. We also give some limits of Minda-type for SK-metrics near the origin. Combining these limits with the Ahlfors' lemma, we provide some observations SK-metrics.

math.CV↗

arXiv2013

Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities

The explicit formula for the hyperbolic metric $λ_{α,\,β,\,γ}(z)|dz|$ on the thrice-punctured sphere $\mathbb{P} \backslash \{z_1,\,z_2,\,z_3\}$ with singularities of order $α,\,β,\,γ\leq 1$ with $α+β+γ>2$ at $z_1,\,z_2,\,z_3$ was given by Kraus, Roth and Sugawa in \cite{Rothhyper}. In this paper we investigate the asymptotic properties of the higher order derivatives of $λ_{α,\,β,\,γ}(z)$ near the singularity and give some more precise description for the asymptotic behavior.

math.CV↗