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Aljoša Peperko

Publications and source records attributed to Aljoša Peperko.

16 recordsLinked to original sources
arXiv2026

Access graph: a novel graph representation of public transport networks for accessibility analysis

Accessibility, defined as travel impedance between spatially dispersed opportunities for activity, is one of the main determinants of public transport use. In-depth understanding of its properties is crucial for optimal public transport systems planning and design. Although the concept has been around for decades and there is a large body of literature on accessibility operationalisation and measurement, a unified approach is lacking. To this end, we introduce a novel graph representation of public transport networks, termed the Access Graph, or A-space, based on the generalised travel times between nodes. We introduce an edge between two nodes in the access graph if the travel time between them is below a certain threshold time budget. In this representation, node degree directly measures the number of nodes reachable within a predetermined time, reproducing the cumulative opportunities measure of access at each specific value of the time budget. We study the threshold-dependent degree distribution of the access graph, focusing on the average degree and the changes in distributions between consecutive time steps. We define a set of accessibility indicators, as well as access equity indicators. The indicators are observed at two characteristic times; the first is based on the evolution of access graph topology and pertaining to the point of degree saturation, reflecting system performance, and the second from the passengers' perspective. We apply the methodology to a dataset of 51 metro networks worldwide. The new representation addresses accessibility at the network structure level, offering a conceptual framework for unified accessibility studies.

physics.soc-ph↗
arXiv2026

Sherman-Takeda type theorems for locally C*-algebras

In this article, we will first establish some density results for a locally $C^*$-algebra $\mathcal A$ and then identify a property, called Kaplansky density property (KDP). We then give a induced faithful continuous $*$-representation $φ$ of $\mathcal A^{**}$ (equipped with unique Arens product) on the space $B_{loc}(\mathcal H)$ such that $φ(\mathcal A^{**})\subset \overline{π(\mathcal A)}^{WOT}$, where $π:\mathcal A\to B_{loc}(\mathcal H)$ is the associated universal $*$-representation and $\mathcal H$ is the associated locally Hilbert space. Finally we show that for a Fréchet locally $C^*$-algebra $\mathcal A$ possessing KDP, the second strong dual is algebraically and topologically $*$-isomorphic to $ \overline{π(\mathcal A)}^{WOT}$, which is a direct analogue of the classical Sherman-Takeda theorem for $C^*$-algebras. We shall also observe the joint continuity of some associated bilinear maps in the running.

math.OA↗
arXiv2025

The Berger-Wang formula for order-preserving homogeneous maps on cones

We prove that the joint spectral radius and generalized spectral radius are equal for any bounded, equicontinuous family of order-preserving, homogeneous maps on a polyhedral cone. We also consider conditions which guarantee that the semigroup generated by a family of order-preserving, homogeneous maps is bounded when its generalized spectral radius $r(\mathcal{A}) = 1$. Finally, we extend the notions of joint and generalized spectral subradii to the setting of homogeneous maps on wedges.

math.FA↗
arXiv2024

Calculating the sequences behind a hexagonal lattice based equal circle packing in the Euclidian plane

The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take form of either polynomials or rational functions. If the circle packing area is limited with a circle, the packing densities tend to decrease with increasing number of the packed circles and converge to values lower than π/(2\sqrt{3}). In cases with packing areas limited by equilateral triangles or equilateral hexagons the packing densities tend to increase with increasing number of the packed circles and converge to π/(2\sqrt{3}). The equilateral hexagons are shown to be the preferred equal circle packing surface areas with practical applications searching for high equal circle packing densities, since the packing densities with circle packing inside equilateral hexagons converge faster to π/(2\sqrt{3}) than in the case of equilateral triangle packing surface areas.

math.MG↗
arXiv2022

Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators

We prove new inequalities and equalities for the generalized and the joint spectral radius (and their essential versions) of Hadamard (Schur) geometric means of bounded sets of positive kernel operators on Banach function spaces. In the case of nonnegative matrices that define operators on Banach sequences we obtain additional results. Our results extend results of several authors that appeared relatively recently.

math.FA↗
arXiv2017

Lower spectral radius and spectral mapping theorem for suprema preserving mappings

We study Lipschitz, positively homogeneous and finite suprema preserving mappings defined on a max-cone of positive elements in a normed vector lattice. We prove that the lower spectral radius of such a mapping is always a minimum value of its approximate point spectrum. We apply this result to show that the spectral mapping theorem holds for the approximate point spectrum of such a mapping. By applying this spectral mapping theorem we obtain new inequalites for the Bonsall cone spectral radius of max type kernel operators.

math.SP↗
arXiv2016

On the Bonsall cone spectral radius and the approximate point spectrum

We study the Bonsall cone spectral radius and the approximate point spectrum of (in general non-linear) positively homogeneous, bounded and supremum preserving maps, defined on a max-cone in a given normed vector lattice. We prove that the Bonsall cone spectral radius of such maps is always included in its approximate point spectrum. Moreover, the approximate point spectrum always contains a (possibly trivial) interval. Our results apply to a large class of (nonlinear) max-type operators. We also generalize a known result that the spectral radius of a positive (linear) operator on a Banach lattice is contained in the approximate point spectrum. Under additional generalized compactness type assumptions our results imply Krein-Rutman type results.

math.SP↗
arXiv2016

Bounds on the joint and generalized spectral radius of Hadamard geometric mean of bounded sets of positive kernel operators

Let $Ψ_1, \ldots Ψ_m$ be bounded sets of positive kernel operators on a Banach function space $L$. We prove that for the generalized spectral radius $ρ$ and the joint spectral radius $\hatρ$ the inequalities $$ρ\left(Ψ_1 ^{\left( \frac{1}{m} \right)} \circ \cdots \circ Ψ_m ^{\left( \frac{1}{m} \right)} \right) \le ρ(Ψ_1 Ψ_2 \cdots Ψ_m) ^{\frac{1}{m}},$$ $$\hatρ \left(Ψ_1 ^{\left( \frac{1}{m} \right)} \circ \cdots \circ Ψ_m ^{\left( \frac{1}{m} \right)} \right) \le \hatρ (Ψ_1 Ψ_2 \cdots Ψ_m) ^{\frac{1}{m}}$$ hold, where $Ψ_1 ^{\left( \frac{1}{m} \right)} \circ \cdots \circ Ψ_m ^{\left( \frac{1}{m} \right)}$ denotes the Hadamard (Schur) geometric mean of the sets $Ψ_1, \ldots , Ψ_m$.

math.SP↗
arXiv2016

Inequalities on the spectral radius, operator norm and numerical radius of Hadamard weighted geometric mean of positive kernel operators

Recently, several authors have proved inequalities on the spectral radius $ρ$, operator norm $\|\cdot\|$ and numerical radius of Hadamard products and ordinary products of non-negative matrices that define operators on sequence spaces, or of Hadamard geometric mean and ordinary products of positive kernel operators on Banach function spaces. In the present article we generalize and refine several of these results. In particular, we show that for a Hadamard geometric mean $A ^{\left( \frac{1}{2} \right)} \circ B ^{\left( \frac{1}{2} \right)}$ of positive kernel operators $A$ and $B$ on a Banach function space $L$, we have $$ ρ\left(A^{(\frac{1}{2})} \circ B^{(\frac{1}{2})} \right) \le ρ\left((AB)^{(\frac{1}{2})} \circ (BA)^{(\frac{1}{2})}\right)^{\frac{1}{2}} \le ρ(AB)^{\frac{1}{2}}.$$ In the special case $L=L^2(X, μ)$ we also prove that $$\|A^{(\frac{1}{2})} \circ B^{(\frac{1}{2})} \| \le ρ\left ( (A^* B ) ^{(\frac{1}{2})}\circ (B ^* A)^{(\frac{1}{2})}\right)^{\frac{1}{2}} \le ρ(A^* B )^{\frac{1}{2}}.$$

math.SP↗
arXiv2016

Semigroups of max-plus linear operators

We define strongly continuous max-additive and max-plus linear operator semigroups and study their main properties. We present some important examples of such semigroups coming from non-linear evolution equations.

math.FA↗
arXiv2015

Inequalities on the spectral radius and the operator norm of Hadamard products of positive operators on sequence spaces

Relatively recently, K.M.R. Audenaert (2010), R.A. Horn and F. Zhang (2010), Z. Huang (2011), A.R. Schep (2011), A. Peperko (2012), D. Chen and Y. Zhang (2015) have proved inequalities on the spectral radius and the operator norm of Hadamard products and ordinary matrix products of finite and infinite non-negative matrices that define operators on sequence spaces. In the current paper we extend and refine several of these results and also prove some analogues for the numerical radius. Some inequalities seem to be new even in the case of $n\times n$ non-negative matrices.

math.FA↗