arXiv subjects

Andrea Marino

Publications and source records attributed to Andrea Marino.

31 records · Page 2Linked to original sources

arXiv2021

Possible multi-orbital ground state in CeCu$_2$Si$_2$

The crystal-field ground state wave function of CeCu$_2$Si$_2$ has been investigated with linear polarized $M$-edge x-ray absorption spectroscopy from 250mK to 250K, thus covering the superconducting ($T_{\text{c}}$=0.6K), the Kondo ($T_{\text{K}}$$\approx$20K) as well as the Curie-Weiss regime. The comparison with full-multiplet calculations shows that the temperature dependence of the experimental linear dichroism is well explained with a $Γ_7^{(1)}$ crystal-field ground-state and the thermal population of excited states at around 30meV. The crystal-field scheme does not change throughout the entire temperature range thus making the scenario of orbital switching unlikely. Spectroscopic evidence for the presence of the Ce 4$f^0$ configuration in the ground state is consistent with the possibility for a multi-orbital character of the ground state. We estimate from the Kondo temperature and crystal-field splitting energies that several percents of the higher lying $Γ_6$ state and $Γ_7^{(2)}$ crystal-field states are mixed into the primarily $Γ_7^{(1)}$ ground state. This estimate is also supported by re-normalized band-structure calculations that uses the experimentally determined crystal-field scheme.

cond-mat.str-el↗

arXiv2020

Dual nature of 5$f$ electrons in the isostructural UM$_2$Si$_2$ family: from antiferro- to Pauli paramagnetism via hidden order

Using inelastic x-ray scattering beyond the dipole limit and hard x-ray photoelectron spectroscopy we establish the dual nature of the U $5f$ electrons in UM$_2$Si$_2$ (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U $5f^2$ configuration with the $Γ_1^{(1)}$ and $Γ_2$ quasi-doublet symmetry. The amount of the U 5$f^3$ configuration, however, varies considerably across the UM$_2$Si$_2$ series, indicating an increase of U5$f$ itineracy in going from M=Pd to Ni to Ru, and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in UPd$_2$Si$_2$ and UNi$_2$Si$_2$, the availability of orbital degrees of freedom needed for the hidden order in URu$_2$Si$_2$ to occur, as well as the appearance of Pauli paramagnetism in UFe$_2$Si$_2$. A unified and systematic picture of the U$M_2$Si$_2$ compounds may now be drawn, thereby providing suggestions for new experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered ThCr$_2$Si$_2$ structure.

cond-mat.str-el↗

arXiv2020

Efficient Estimation of Graph Trussness

A $k$-truss is an edge-induced subgraph $H$ such that each of its edges belongs to at least $k-2$ triangles of $H$. This notion has been introduced around ten years ago in social network analysis and security, as a form of cohesive subgraph that is rich of triangles and less stringent than the clique. The \emph{trussness} of a graph is the maximum $k$ such that a $k$-truss exists. The problem of computing $k$-trusses has been largely investigated from the practical and engineering point of view. On the other hand, the theoretical side of the problem has received much less attention, despite presenting interesting challenges. The existing methods share a common design, based on iteratively removing the edge with smallest support, where the support of an edge is the number of triangles containing it. The aim of this paper is studying algorithmic aspects of graph trussness. While it is possible to show that the time complexity of computing exactly the graph trussness and that of counting/listing all triangles is inherently the same, we provide efficient algorithms for estimating its value, under suitable conditions, with significantly lower complexity than the exact approach. In particular, we provide a $(1 \pm ε)$-approximation algorithm that is asymptotically faster than the exact approach, on graphs which contain $ω(m \, polylog(n))$ triangles, and has the same running time on graphs that do not. For the latter case, we also show that it is impossible to obtain an approximation algorithm with faster running time than the one of the exact approach when the number of triangles is $O(m)$, unless well known conjectures on triangle-freeness and Boolean matrix multiplication are false.

cs.DS↗

arXiv2020

Edge-Disjoint Branchings in Temporal Graphs

A temporal digraph ${\cal G}$ is a triple $(G, γ, λ)$ where $G$ is a digraph, $γ$ is a function on $V(G)$ that tells us the timestamps when a vertex is active, and $λ$ is a function on $E(G)$ that tells for each $uv \in E(G)$ when $u$ and $v$ are linked. Given a static digraph $G$, and a subset $R\subseteq V(G)$, a spanning branching with root $R$ is a subdigraph of $G$ that has exactly one path from $R$ to each $v\in V(G)$. In this paper, we consider the temporal version of Edmonds' classical result about the problem of finding $k$ edge-disjoint spanning branchings respectively rooted at given $R_1,\cdots,R_k$. We introduce and investigate different definitions of spanning branchings, and of edge-disjointness in the context of temporal graphs. A branching ${\cal B}$ is vertex-spanning if the root is able to reach each vertex $v$ of $G$ at some time where $v$ is active, while it is temporal-spanning if $v$ can be reached from the root at every time where $v$ is active. On the other hand, two branchings ${\cal B}_1$ and ${\cal B}_2$ are edge-disjoint if they do not use the same edge of $G$, and are temporal-edge-disjoint if they can use the same edge of $G$ but at different times. This lead us to four definitions of disjoint spanning branchings and we prove that, unlike the static case, only one of these can be computed in polynomial time, namely the temporal-edge-disjoint temporal-spanning branchings problem, while the other versions are $\mathsf{NP}$-complete, even under very strict assumptions.

cs.DS↗

arXiv2018

Listing Maximal Subgraphs in Strongly Accessible Set Systems

Algorithms for listing the subgraphs satisfying a given property (e.g.,being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an indicator F, subset of 2^U, of which subsets of U have the required property. For the problem of listing all sets in F maximal under inclusion, the ambitious goal is to cover a large class of set systems, preserving at the same time the efficiency of the enumeration. Among the existing algorithms, the best-known ones list the maximal subsets in time proportional to their number but may require exponential space. In this paper we improve the state of the art in two directions by introducing an algorithmic framework that, under standard suitable conditions, simultaneously (i) extends the class of problems that can be solved efficiently to strongly accessible set systems, and (ii) reduces the additional space usage from exponential in |U| to stateless, thus accounting for just O(q) space, where q <= |U| is the largest size of a maximal set in F

cs.DM↗

arXiv2017

Computing top-k Closeness Centrality Faster in Unweighted Graphs

Given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $\frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the $k$ most central vertices has been deeply analysed in the last decade. However, this problem is computationally not easy, especially for large networks: in the first part of the paper, we prove that it is not solvable in time $Ø(|E|^{2-ε})$ on directed graphs, for any constant $ε>0$, under reasonable complexity assumptions. Furthermore, we propose a new algorithm for selecting the $k$ most central nodes in a graph: we experimentally show that this algorithm improves significantly both the textbook algorithm, which is based on computing the distance between all pairs of vertices, and the state of the art. For example, we are able to compute the top $k$ nodes in few dozens of seconds in real-world networks with millions of nodes and edges. Finally, as a case study, we compute the $10$ most central actors in the IMDB collaboration network, where two actors are linked if they played together in a movie, and in the Wikipedia citation network, which contains a directed edge from a page $p$ to a page $q$ if $p$ contains a link to $q$.

cs.DS↗

arXiv2016

Sums of Multivariate Polynomials in Finite Subgroups

Let $R$ be a commutative ring, $f \in R[X_1,\ldots,X_k]$ a multivariate polynomial, and $G$ a finite subgroup of the group of units of $R$ satisfying a certain constraint, which always holds if $R$ is a field. Then, we evaluate $\sum f(x_1,\ldots,x_k)$, where the summation is taken over all pairwise distinct $x_1,\ldots,x_k \in G$. In particular, let $p^s$ be a power of an odd prime, $n$ a positive integer coprime with $p-1$, and $a_1,\ldots,a_k$ integers such that $φ(p^s)$ divides $a_1+\cdots+a_k$ and $p-1$ does not divide $\sum_{i \in I}a_i$ for all non-empty proper subsets $I\subseteq \{1,\ldots,k\}$; then $$ \sum x_1^{a_1}\cdots x_k^{a_k} \equiv \frac{φ(p^s)}{\mathrm{gcd}(n,φ(p^s))}(-1)^{k-1}(k-1)! \,\,\bmod{p^s}, $$ where the summation is taken over all pairwise distinct $n$-th residues $x_1,\ldots,x_k$ modulo $p^s$ coprime with $p$.

math.NT↗

arXiv2016

BUbiNG: Massive Crawling for the Masses

Although web crawlers have been around for twenty years by now, there is virtually no freely available, opensource crawling software that guarantees high throughput, overcomes the limits of single-machine systems and at the same time scales linearly with the amount of resources available. This paper aims at filling this gap, through the description of BUbiNG, our next-generation web crawler built upon the authors' experience with UbiCrawler [Boldi et al. 2004] and on the last ten years of research on the topic. BUbiNG is an opensource Java fully distributed crawler; a single BUbiNG agent, using sizeable hardware, can crawl several thousands pages per second respecting strict politeness constraints, both host- and IP-based. Unlike existing open-source distributed crawlers that rely on batch techniques (like MapReduce), BUbiNG job distribution is based on modern high-speed protocols so to achieve very high throughput.

cs.IR↗

arXiv2015

Fast and Simple Computation of Top-k Closeness Centralities

Closeness is an important centrality measure widely used in the analysis of real-world complex networks. In particular, the problem of selecting the k most central nodes with respect to this measure has been deeply analyzed in the last decade. However, even for not very large networks, this problem is computationally intractable in practice: indeed, Abboud et al have recently shown that its complexity is strictly related to the complexity of the All-Pairs Shortest Path (in short, APSP) problem, for which no subcubic "combinatorial" algorithm is known. In this paper, we propose a new algorithm for selecting the k most closeness central nodes in a graph. In practice, this algorithm significantly improves over the APSP approach, even though its worst-case time complexity is the same. For example, the algorithm is able to compute the top k nodes in few dozens of seconds even when applied to real-world networks with millions of nodes and edges. We will also experimentally prove that our algorithm drastically outperforms the most recently designed algorithm, proposed by Olsen et al. Finally, we apply the new algorithm to the computation of the most central actors in the IMDB collaboration network, where two actors are linked if they played together in a movie.

cs.DS↗

arXiv2015

Enumerating Cyclic Orientations of a Graph

Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic orientations has been addressed in the literature. In this paper, we pose the problem of efficiently enumerating all the \emph{cyclic} orientations of an undirected connected graph with $n$ vertices and $m$ edges, observing that it cannot be solved using algorithmic techniques previously employed for enumerating acyclic orientations.We show that the problem is of independent interest from both combinatorial and algorithmic points of view, and that each cyclic orientation can be listed with $\tilde{O}(m)$ delay time. Space usage is $O(m)$ with an additional setup cost of $O(n^2)$ time before the enumeration begins, or $O(mn)$ with a setup cost of $\tilde{O}(m)$ time.

cs.DS↗

arXiv2014

Entity-Linking via Graph-Distance Minimization

Entity-linking is a natural-language-processing task that consists in identifying the entities mentioned in a piece of text, linking each to an appropriate item in some knowledge base; when the knowledge base is Wikipedia, the problem comes to be known as wikification (in this case, items are wikipedia articles). One instance of entity-linking can be formalized as an optimization problem on the underlying concept graph, where the quantity to be optimized is the average distance between chosen items. Inspired by this application, we define a new graph problem which is a natural variant of the Maximum Capacity Representative Set. We prove that our problem is NP-hard for general graphs; nonetheless, under some restrictive assumptions, it turns out to be solvable in linear time. For the general case, we propose two heuristics: one tries to enforce the above assumptions and another one is based on the notion of hitting distance; we show experimentally how these approaches perform with respect to some baselines on a real-world dataset.

cs.DS↗

arXiv2013

Synchronous Context-Free Grammars and Optimal Linear Parsing Strategies

Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed translation schemata, are unlike context-free grammars in that they do not have a binary normal form. In general, parsing with SCFGs takes space and time polynomial in the length of the input strings, but with the degree of the polynomial depending on the permutations of the SCFG rules. We consider linear parsing strategies, which add one nonterminal at a time. We show that for a given input permutation, the problems of finding the linear parsing strategy with the minimum space and time complexity are both NP-hard.

cs.FL↗

arXiv2012

Optimal Listing of Cycles and st-Paths in Undirected Graphs

We present the first optimal algorithm for the classical problem of listing all the cycles in an undirected graph. We exploit their properties so that the total cost is the time taken to read the input graph plus the time to list the output, namely, the edges in each of the cycles. The algorithm uses a reduction to the problem of listing all the paths from a vertex s to a vertex t which we also solve optimally.

cs.DS↗