Rok Požar

University of Primorska | UP · Department of Mathematics

The view of the human brain as a complex network has led to considerable advances in understanding the brain’s network organization during rest and task, in both health and disease. Here, we propose that examining brain networks within the task aftereffect model, in which we compare resting-state networks immediately before and after a cognitive en...

Recently, we have shown a significant decrease in resting‐state EEG (rsEEG) spectral power at post‐task as compared to pre‐task cognitive engagement in older adults. Further, older adults with mild cognitive impairment (MCI) showed greater decreases in rsEEG in temporal and central cortical regions at post‐task than healthy controls (HC). Here, we...

The d $d$‐Simultaneous Conjugacy problem in the symmetric group S n ${S}_{n}$ asks whether there exists a permutation τ ∈ S n $\tau \in {S}_{n}$ such that b j = τ − 1 a j τ ${b}_{j}={\tau }^{-1}{a}_{j}\tau $ holds for all j = 1 , 2 , … , d $j=1,2,\ldots ,d$, where a 1 , a 2 , … , a d ${a}_{1},{a}_{2},\ldots ,{a}_{d}$ and b 1 , b 2 , … , b d ${b}_{1...

The $d$-Simultaneous Conjugacy problem in the symmetric group $S_n$ asks whether there exists a permutation $\tau \in S_n$ such that $b_j = \tau^{-1}a_j \tau$ holds for all $j = 1,2,\ldots, d$, where $a_1, a_2,\ldots , a_d$ and $b_1, b_2,\ldots , b_d$ are given sequences of permutations in $S_n$. The time complexity of existing algorithms for solvi...

Community-dwelling African American elders are twice as likely to develop mild cognitive impairment (MCI) or Alzheimer’s disease and related dementias than older white Americans and therefore represent a significant at-risk group in need of early monitoring. More extensive imaging or cerebrospinal fluid studies represent significant barriers due to...

Given a finite sequence $a_1, a_2,\ldots, a_d$ of $d$ permutations in the symmetric group $S_n$, and a permutation word $k_1k_2\cdots k_{m}$ over the alphabet $\{1,2,\ldots, d\}$, computation of the product $a_{k_1}a_{k_2}\cdots a_{k_{m}}$ in a straightforward manner takes $O(n m)$ time. However, it appears that this multiplication is such an eleme...

Background Age and disease related cognitive declines have important socioeconomic implications. Identifying those who are at risk and the underlying mechanisms for accelerated cognitive decline are vital for guiding interventions and improving early prediction of dementia. We propose a novel approach for risk prediction using repeated electrophysi...

https://deepblue.lib.umich.edu/bitstream/2027.42/152558/1/alzjjalz2019063490.pdf

https://deepblue.lib.umich.edu/bitstream/2027.42/153097/1/alzjjalz201908117.pdf

Let p: X → X be a regular covering projection of connected graphs, where CTP denotes the group of covering transformations. Suppose that a group G ≤ AutX lifts along P to a group G ≤ Aut X. The corresponding short exact sequence id → CTP G → G → id is split sectional over a G-invariant subset of vertices Ω ⊆ V (X) if there exists a sectional comple...

Let U be a finitely presented group with a normal subgroup F, and let H be a finite group. We present an effective method for constructing all U-stable epimorphisms from F onto H; that is, epimorphisms whose kernels are normal in U. Our strategy is an adaptation of the algorithm for determining all epimorphisms from a finitely presented group onto...

A connected graph whose automorphism group acts transitively on the edges and vertices, but not on the set of ordered pairs of adjacent vertices of the graph is called half-arc-transitive. It is well known that the valence of a half-arc-transitive graph is even and at least four. Several infinite families of half-arc-transitive graphs of valence fo...

Let p: (X) over tilde -> X be a regular covering projection of connected graphs with the group of covering transformations CTp being abelian. Assuming that a group of automorphisms G <= Aut X lifts along p to a group (G) over tilde <= Aut (X) over tilde, the problem whether the corresponding exact sequence id -> CTp -> (G) over tilde -> G -> id spl...

Let a group of automorphisms lift along a regular covering projection of connected graphs given combinatorially by means of voltages. The data that determine the lifted group and its action are then conveniently encoded in terms of voltages as well. Along these lines, an algorithm for testing whether the lifted group is a split extension of the gro...

A connected graph whose automorphism group acts transitively on the edges and vertices, but not on the set of ordered pairs of adjacent vertices of the graph is called half-arc-transitive. It is well known that the valence of a half-arc-transitive graph is even and at least four. Several infinite families of half-arc-transitive graphs of valence fo...

Given a connected graph X and a group G of its automorphisms we first introduce an approach for constructing all pairwise nonequivalent connected solvable regular coverings ℘:X˜→X (that is, with a solvable group of covering transformations CT(℘)CT(℘)) along which G lifts, up to a prescribed order n of X˜. Next, given a connected solvable regular co...

Covering techniques have recently emerged as an effective tool used for classification of several infinite families of connected symmetric graphs. One commonly encountered technique is based on the concept of lifting groups of automorphisms along regular covering projections ℘:X ˜→X. Efficient computational methods are known for regular covers with...