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Social networks inherently exhibit complex relationships that can be positive or negative, as well as directional. Understanding balance in these networks is crucial for unraveling social dynamics, yet traditional theories struggle to incorporate directed interactions. This perspective presents a comprehensive roadmap for understanding balance in signed directed networks, extending traditional balance theory to account for directed interactions. Balance is indicated by the enrichment of higher-order patterns like triads compared to an adequate null model, where the network is randomized with some key aspects being preserved. Finding appropriate null models has been a challenging task even without considering directionality, which largely expands the space of potential null models. Recently, it has been shown that in the undirected case both the network topology and the signed degrees serve as key factors to preserve. Therefore, we introduce a maximally constrained null model that preserves the directed topology as well as node-level features given by the signed unidirectional, reciprocated, and conflicting node degrees. Our null model is based on the maximum-entropy principle and reveals consistent patterns across large-scale social networks. We also consider directed generalizations of balance theory and find that the observed patterns are well aligned with two proposed directed notions of strong balance. Our approach not only unveils balance in signed directed networks but can also serve as a starting point towards generative models of signed directed social networks, advancing our understanding of complex social systems and their dynamics.

In a quantum communication network, links represent entanglement between qubits located at different nodes. Even if two nodes are not directly linked by shared entanglement, communication channels can be established between them via quantum routing protocols. However, in contrast to classical communication networks, each communication event removes all participating links along the communication path, disrupting the quantum network. Here, we propose a simple model, where randomly selected pairs of nodes communicate through shortest paths. Each time such a path is used, all participating links are eliminated, leading to a correlated percolation process that we call ``path percolation.'' We study path percolation both numerically and analytically and present the phase diagram of the steady states as a function of the rate at which new links are being added to the quantum communication network. As a key result, the steady state is found to be independent from the initial network topology when new link are added randomly between disconnected components. We close by discussing extensions of path percolation and their potential applications., Comment: 10 pages, 5 figures

Volumetric brain reconstructions provide an unprecedented opportunity to gain insights into the complex connectivity patterns of neurons in an increasing number of organisms. Here, we model and quantify the complexity of the resulting neural connectomes in the fruit fly, mouse, and human and unveil a simple set of shared organizing principles across these organisms. To put the connectomes in a physical context, we also construct contactomes, the network of neurons in physical contact in each organism. With these, we establish that physical constraints -- either given by pairwise distances or the contactome -- play a crucial role in shaping the network structure. For example, neuron positions are highly optimal in terms of distance from their neighbors. However, spatial constraints alone cannot capture the network topology, including the broad degree distribution. Conversely, the degree sequence alone is insufficient to recover the spatial structure. We resolve this apparent conflict by formulating scalable maximum entropy models, incorporating both types of constraints. The resulting generative models have predictive power beyond the input data, as they capture several additional biological and network characteristics, like synaptic weights and graphlet statistics., Comment: 24 pages, 20 figures

Here, the entanglement entropy is calculated at the quantum multicritical point of the random transverse-field Ising model (RTIM). We use an efficient implementation of the strong disorder renormalization group method in two and three dimensions for two types of disorder. For cubic subsystems we find a universal logarithmic corner contribution to the area law b*ln(l) that is independent of the form of disorder. Our results agree qualitatively with those at the quantum critical points of the RTIM, but with new b prefactors due to having both geometric and quantum fluctuations at play. By studying the vicinity of the multicritical point, we demonstrate that the corner contribution serves as an `entanglement susceptibility', a useful tool to locate the phase transition and to measure the correlation length critical exponents., Comment: 6 pages, 4 figures, 1 table

Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We first map the problem of quantum communication with local usage of memories into a classical continuum percolation model. Then, we show that this mapping can be improved through a cooperation of entanglement distillation and relay protocols via remote access to distributed memories. This improved mapping, which we term $\alpha$-percolation, can be formulated in terms of graph-merging rules, analogous to the decimation rules of the renormalization group treatment of disordered quantum magnets. These rules can be performed in any order, yielding the same optimal result, which is characterized by the emergence of a ``positive feedback'' mechanism and the formation of spatially disconnected ``hopping'' communication components -- both marking significant improvements in quantum network connectivity., Comment: 6 pages, 3 figures

A graph $\Gamma$ is said to be unstable if for the direct product $\Gamma \times K_2$, $Aut(\Gamma \times K_2)$ is not isomorphic to $Aut(\Gamma) \times \mathbb{Z}_2$. In this paper we show that a connected and non-bipartite Cayley graph $Cay(H,S)$ is unstable if and only if the set $S \times \{1\}$ belongs to a Schur ring over the group $H \times \mathbb{Z}_2$ having certain properties. The Schur rings with these properties are characterized if $H$ is an abelian group of odd order or a cyclic group of twice odd order. As an application, a short proof is given for the result of Witte Morris stating that every connected unstable Cayley graph on an abelian group of odd order has twins (Electron.~J.~Combin, 2021). As another application, sufficient and necessary conditions are given for a connected and non-bipartite circulant graph of order $2p^e$ to be unstable, where $p$ is an odd prime and $e \ge 1$.

In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends on microscopic details of the system. However, at criticality, there is often an additional nonlinearity of the form $b\ln(\ell)$, originating from the endpoints of the line segment. By performing large scale Monte Carlo simulations of both 2$d$ and 3$d$ percolation, we find that $b$ is universal and depends only on the angles encountered at the endpoints of the line segment intersecting the sample. Our findings are further supported by analytic arguments in 2$d$, building on results in conformal field theory. Being broadly applicable, cluster tomography can be an efficient tool to detect phase transitions and to characterize the corresponding universality class in classical or quantum systems with a relevant cluster structure., Comment: 11 pages, 7 figures

Recent cellular-level volumetric brain reconstructions have revealed high levels of anatomic complexity. Determining which structural aspects of the brain to focus on, especially when comparing with computational models and other organisms, remains a major challenge. Here we quantify aspects of this complexity and show evidence that brain anatomy satisfies universal scaling laws, establishing the notion of structural criticality in the cellular structure of the brain. Our framework builds upon understanding of critical systems to provide clear guidance in selecting informative structural properties of brain anatomy. As an illustration, we obtain estimates for critical exponents in the human, mouse and fruit fly brains and show that they are consistent between organisms, to the extent that data limitations allow. Such universal quantities are robust to many of the microscopic details of individual brains, providing a key step towards generative computational brain models, and also clarifying in which sense one animal may be a suitable anatomic model for another., Comment: 17 pages, 10 figures

A graph $\Gamma$ is said to be stable if for the direct product $\Gamma\times\mathbf{K}_2$, ${\rm Aut}(\Gamma \times \mathbf{K}_2)$ is isomorphic to ${\rm Aut}(\Gamma) \times \mathbb{Z}_2$; otherwise, it is called unstable. An unstable graph is called non-trivially unstable when it is not bipartite and no two vertices have the same neighborhood. Wilson described nine families of unstable Rose Window graphs and conjectured that these contain all non-trivially unstable Rose Window graphs (2008). In this paper we show that the conjecture is true.

Studying significant network patterns, known as graphlets (or motifs), has been a popular approach to understand the underlying organizing principles of complex networks. Statistical significance is routinely assessed by comparing to null models that randomize the connections while preserving some key aspects of the data. However, in signed networks, capturing both positive (friendly) and negative (hostile) relations, the results have been controversial and also at odds with the classical theory of structural balance. We show that this is largely due to the fact that large-scale signed networks exhibit a poor correlation between the number of positive and negative ties of each node. As a solution, here we propose a null model based on the maximum entropy framework that preserves both the signed degrees and the network topology (STP randomization). With STP randomization the results change qualitatively and most social networks consistently satisfy strong structural balance, both at the level of triangles and larger graphlets. We propose a potential underlying mechanism of the observed patterns in signed social networks and outline further applications of STP randomization.

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions., Comment: 19 pages, 1 figure, 1 box

A skew morphism of a finite group $A$ is a permutation $\varphi$ of $A$ fixing the identity element and for which there is an integer-valued function $\pi$ on $A$ such that $\varphi(ab)=\varphi(a)\varphi^{\pi(a)}(b)$ for all $a, b \in A$. A skew morphism $\varphi$ of $A$ is smooth if the associated power function $\pi$ is constant on the orbits of $\varphi$, that is, $\pi(\varphi(a))\equiv\pi(a)\pmod{|\varphi|}$ for all $a\in A$. In this paper we show that every skew morphism of a cyclic group of order $n$ is smooth if and only if $n=2^en_1$, where $0 \le e \le 4$ and $n_1$ is an odd square-free number. A partial solution to a similar problem on non-cyclic abelian groups is also given.

In the emerging quantum internet, complex network topology could lead to efficient quantum communication and enhanced robustness against failures. However, there are some concerns about complexity in quantum communication networks, such as potentially limited end-to-end transmission capacity. These challenges call for model systems in which the feasibility and impact of complex network topology on quantum communication protocols can be explored. Here, we present a theoretical model for complex quantum communication networks on a lattice of spins, wherein entangled spin clusters in interacting quantum spin systems serve as communication links between appropriately selected regions of spins. Specifically, we show that ground state Greenberger-Horne-Zeilinger clusters of the two-dimensional random transverse Ising model can be used as communication links between regions of spins, and we show that the resulting quantum networks can have complexity comparable to that of the classical internet. Our work provides an accessible generative model for further studies towards determining the network characteristics of the emerging quantum internet., Comment: 16 pages, 3 figures

Motivated by the compound ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider the Ising chain with random couplings and in the presence of simultaneous random transverse and longitudinal fields, and study its low-energy properties at zero temperature by the strong disorder renormalization group approach. In the absence of longitudinal fields, the system exhibits a quantum-ordered and a quantum-disordered phase separated by a critical point of infinite disorder. When the longitudinal random field is switched on, the ordered phase vanishes and the trajectories of the renormalization group are attracted to two disordered fixed points: one is characteristic of the classical random field Ising chain, the other describes the quantum disordered phase. The two disordered phases are separated by a separatrix that starts at the infinite disorder fixed point and near which there are strong quantum fluctuations., Comment: 12 pages, 8 figures

A finite simple graph $\Gamma$ is called a Nest graph if it is regular of valency $6$ and admits an automorphism $\rho$ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that $\Gamma$ is core-free if no non-trivial subgroup of the group generated by $\rho$ is normal in $\mathrm{Aut}(\Gamma)$. In this paper, we show that, if $\Gamma$ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph $H(2,4)$, the Shrikhande graph and a certain normal $2$-cover of $K_{3,3}$ by $\mathbb{Z}_2^4$., Comment: arXiv admin note: text overlap with arXiv:2111.07982

Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement negativity (${\cal E}$) and mutual information (${\cal I}$) in critical random Ising chains. Both the disorder averaged ${\cal E}$ and ${\cal I}$ are found to be scale-invariant and universal, i.e. independent of the form of disorder. We find a constant ${\cal E}(\alpha)$ and ${\cal I}(\alpha)$ over any distances, using the asymptotically exact strong disorder renormalization group method. Our results are qualitatively different from both those in the clean Ising model and random spin chains of a singlet ground state, like the spin-$\frac{1}{2}$ random Heisenberg chain and the random XX chain. While for random singlet states ${\cal I}(\alpha)/{\cal E}(\alpha)=2$, in the random Ising chain this universal ratio is strongly $\alpha$-dependent. This deviation between systems contrasts with the behavior of the entanglement entropy of a single subsystem, for which the various random critical chains and clean models give the same qualitative behavior. Therefore, studying multipartite entanglement provides additional universal information in random quantum systems, beyond what we can learn from a single subsystem., Comment: 7 pages, 7 figures

With the deployment of 5G networks, standards organizations have started working on the design phase for sixth-generation (6G) networks. 6G networks will be immensely complex, requiring more deployment time, cost and management efforts. On the other hand, mobile network operators demand these networks to be intelligent, self-organizing, and cost-effective to reduce operating expenses (OPEX). Machine learning (ML), a branch of artificial intelligence (AI), is the answer to many of these challenges providing pragmatic solutions, which can entirely change the future of wireless network technologies. By using some case study examples, we briefly examine the most compelling problems, particularly at the physical (PHY) and link layers in cellular networks where ML can bring significant gains. We also review standardization activities in relation to the use of ML in wireless networks and future timeline on readiness of standardization bodies to adapt to these changes. Finally, we highlight major issues in ML use in the wireless technology, and provide potential directions to mitigate some of them in 6G wireless networks., Comment: 6

For a permutation group $G$ acting on a set $V$, a subset $\mathcal{F}$ of $G$ is said to be an intersecting set if for every pair of elements $g,h\in \mathcal{F}$ there exists $v \in V$ such that $g(v) = h(v)$. The intersection density $\rho(G)$ of a transitive permutation group $G$ is the maximum value of the quotient $|\mathcal{F}|/|G_v|$ where $G_v$ is a stabilizer of a point $v\in V$ and $\mathcal{F}$ runs over all intersecting sets in $G$. If $G_v$ is a largest intersecting set in $G$ then $G$ is said to have the Erd\H{o}s-Ko-Rado (EKR)-property. This paper is devoted to the study of transitive permutation groups, with point stabilizers of prime order with a special emphasis given to orders 2 and 3, which do not have the EKR-property. Among other, constructions of infinite family of transitive permutation groups having point stabilizer of order $3$ with intersection density $4/3$ and of infinite families of transitive permutation groups having point stabilizer of order $3$ with arbitrarily large intersection density are given., Comment: 14 pages

In many-body systems with quenched disorder, dynamical observables can be singular not only at the critical point, but in an extended region of the paramagnetic phase as well. These Griffiths singularities are due to rare regions, which are locally in the ordered phase and contribute to a large susceptibility. Here, we study the geometrical properties of rare regions in the transverse Ising model with dilution or with random couplings and transverse fields. In diluted models, the rare regions are percolation clusters, while in random models the ground state consists of a set of spin clusters, which are calculated by the strong disorder renormalization method. We consider the so called energy cluster, which has the smallest excitation energy and calculate its mass and linear extension in one-, two- and three-dimensions. Both average quantities are found to grow logarithmically with the linear size of the sample. Consequently, the rare regions are not compact: for the diluted model they are isotropic and tree-like, while for the random model they are quasi-one-dimensional., Comment: 8 pages, 9 figures

We prove that the direct product of two coprime order elementary abelian groups of rank two, as well as the direct product of a cyclic group of prime order and a cyclic group of square free order are DCI-groups. The latter is a generalization of Muzychuk's result on cyclic groups (J. Combin. Theory Ser. A, 1995)., Comment: 21 pages

Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize explicit counting of even and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction, QLP, using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction., Comment: Keywords: Complex Networks, Quantum Algorithms, Link Prediction, Social Networks, Protein-Protein Interaction Networks

A graph admitting an automorphism with two orbits of the same length is called a bicirculant. Recently, Jajcay et al. initiated the investigation of the edge-transitive bicirculants with the properties that one of the subgraphs induced by the latter orbits is a cycle and the valence is at least $6$ (Electron. J. Combin., 2019). We show that the complement of the Petersen graph is the only such graph whose order is twice an odd number.

Quantum multicritical points (QMCPs) emerge at the junction of two or more quantum phase transitions due to the interplay of disparate fluctuations, leading to novel universality classes. While quantum critical points have been well characterized, our understanding of QMCPs is much more limited, even though they might be less elusive to study experimentally than quantum critical points. Here, we characterize the QMCP of an interacting heterogeneous quantum system in two and three dimensions, the ferromagnetic random transverse-field Ising model (RTIM). The QMCP of the RTIM emerges due to both geometric and quantum fluctuations, studied here numerically by the strong disorder renormalization group method. The QMCP of the RTIM is found to exhibit ultraslow, activated dynamic scaling, governed by an infinite disorder fixed point. This ensures that the obtained multicritical exponents tend to the exact values at large scales, while also being universal -- i.e. independent of the form of disorder -- , providing a solid theoretical basis for future experiments., Comment: 7 pages, 8 figures

Artificial intelligence and data-driven networks will be integral part of 6G systems. In this article, we comprehensively discuss implementation challenges and need for architectural changes in 5G radio access networks for integrating machine learning (ML) solutions. As an example use case, we investigate user equipment (UE) positioning assisted by deep learning (DL) in 5G and beyond networks. As compared to state of the art positioning algorithms used in today's networks, radio signal fingerprinting and machine learning (ML) assisted positioning requires smaller additional feedback overhead; and the positioning estimates are made directly inside the radio access network (RAN), thereby assisting in radio resource management. In this regard, we study ML-assisted positioning methods and evaluate their performance using system level simulations for an outdoor scenario. The study is based on the use of raytracing tool, a 3GPP 5G NR compliant system level simulator and DL framework to estimate positioning accuracy of the UE. We evaluate and compare performance of various DL models and show mean positioning error in the range of 1-1.5m for a 2-hidden layer DL architecture with appropriate feature-modeling. Building on our performance analysis, we discuss pros and cons of various architectures to implement ML solutions for future networks and draw conclusions on the most suitable architecture., Comment: IEEE Open Journal of Vehicular Technology Society. arXiv admin note: substantial text overlap with arXiv:2001.00977

Cellular-connected unmanned aerial vehicle (UAV) has attracted a surge of research interest in both academia and industry. To support aerial user equipment (UEs) in the existing cellular networks, one promising approach is to assign a portion of the system bandwidth exclusively to the UAV-UEs. This is especially favorable for use cases where a large number of UAV-UEs are exploited, e.g., for package delivery close to a warehouse. Although the nearly line-of-sight (LoS) channels can result in higher powers received, UAVs can in turn cause severe interference to each other in the same frequency band. In this contribution, we focus on the uplink communications of massive cellular-connected UAVs. Different power allocation algorithms are proposed to either maximize the minimal spectrum efficiency (SE) or maximize the overall SE to cope with severe interference based on the successive convex approximation (SCA) principle. One of the challenges is that a UAV can affect a large area meaning that many more UAV-UEs must be considered in the optimization problem, which is essentially different from that for terrestrial UEs. The necessity of single-carrier uplink transmission further complicates the problem. Nevertheless, we find that the special property of large coherent bandwidths and coherent times of the propagation channels can be leveraged. The performances of the proposed algorithms are evaluated via extensive simulations in the full-buffer transmission mode and bursty-traffic mode. Results show that the proposed algorithms can effectively enhance the uplink SEs. This work can be considered the first attempt to deal with the interference among massive cellular-connected UAV-UEs with optimized power allocations., Comment: The final version can be found in IEEE Transactions on Vehicular Technology

In this paper, we characterize the finite groups $G$ of even order with the property that for any involution $x$ and element $y$ of $G$, $\langle x, y \rangle$ is isomorphic to one of the following groups: $\mathbb{Z}_2,$ $\mathbb{Z}_2^2$, $\mathbb{Z}_4$, $\mathbb{Z}_6$, $\mathbb{Z}_2 \times \mathbb{Z}_4$, $\mathbb{Z}_2 \times\mathbb{Z}_6$ and $A_4$. As a result, a characterization will be obtained for the finite groups all of whose Cayley graphs of degree $3$ have integral spectrum.

In random quantum magnets, like the random transverse Ising chain, the low energy excitations are localized in rare regions and there are only weak correlations between them. It is a fascinating question whether these correlations are completely irrelevant in the sense of the renormalization group. To answer this question, we calculate the distribution of the excitation energy of the random transverse Ising chain in the disordered Griffiths phase with high numerical precision by the strong disorder renormalization group method and - for shorter chains - by free-fermion techniques. Asymptotically, the two methods give identical results, which are well fitted by the Fr\'echet limit law of the extremes of independent and identically distributed random numbers. Given the finite size corrections, the two numerical methods give very similar results, but they differ from the correction term for uncorrelated random variables. This fact shows that the weak correlations between low-energy excitations in random quantum magnets are not entirely irrelevant., Comment: 10 pages, 4 figures

Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected. This finding indicates a counter-intuitive organization of dynamical correlations, where functional similarity decouples from physical connectivity. We illustrate the phenomena on the example of the Disordered Contact Process (DCP) of infection spreading in heterogeneous systems. We apply numerical simulations and an asymptotically exact renormalization group technique (SDRG) in 1, 2 and 3 dimensional systems as well as in two-dimensional lattices with long-ranged interactions. We conclude that the critical dynamics is well captured by mostly one, highly correlated, but spatially disconnected cluster. Our findings indicate that at criticality the relevant, simultaneously infected sites typically do not directly interact with each other. Due to the similarity of the SDRG equations, our results hold also for the critical behavior of the disordered quantum Ising model, leading to quantum correlated, yet spatially disconnected, magnetic domains., Comment: 9 pages, 6 figures

Cellular-connected unmanned aerial vehicles (UAVs) have recently attracted a surge of interest in both academia and industry. Understanding the air-to-ground (A2G) propagation channels is essential to enable reliable and/or high-throughput communications for UAVs and protect the ground user equipments (UEs). In this contribution, a recently conducted measurement campaign for the A2G channels is introduced. A uniform circular array (UCA) with 16 antenna elements was employed to collect the downlink signals of two different Long Term Evolution (LTE) networks, at the heights of 0-40m in three different, namely rural, urban and industrial scenarios. The channel impulse responses (CIRs) have been extracted from the received data, and the spatial/angular parameters of the multipath components in individual channels were estimated according to a high-resolution-parameter estimation (HRPE) principle. Based on the HRPE results, clusters of multipath components were further identified. Finally, comprehensive spatial channel characteristics were investigated in the composite and cluster levels at different heights in the three scenarios., Comment: 17pages. This work has been accepted by IEEE JSAC

Power control is becoming increasingly essential for the fifth-generation (5G) and beyond systems. An example use-case, among others, is the unmanned-aerial-vehicle (UAV) communications where the nearly line-of-sight (LoS) radio channels may result in very low signal-to-interference-plus-noise ratios (SINRs). Investigations in [1] proposed to efficiently and reliably solve this kind of non-convex problem via a series of geometrical programmings (GPs) using condensation approximation. However, it is only applicable for a small-scale network with several communication pairs and practically infeasible with more (e.g. tens of) nodes to be jointly optimized. We therefore in this paper aim to provide new insights into this problem. By properly introducing auxiliary variables, the problem is transformed to an equivalent form which is simpler and more intuitive for condensation. A novel condensation method with linear complexity is also proposed based on the form. The enhancements make the GP-based power control feasible for both small-and especially large-scale networks that are common in 5G and beyond. The algorithm is verified via simulations. A preliminary case study of uplink UAV communications also shows the potential of the algorithm., Comment: Accepted by IEEE Transactions on Vehicular Technology

Antenna systems serve to absorb light and to transmit excitation energy to the reaction center (RC) in photosynthetic organisms. As the emitted (bacterio)chlorophyll fluorescence competes with the photochemical utilization of the excitation, the measured fluorescence yield is informed by the migration of the excitation in the antenna. In this work, the fluorescence yield concomitant with the oxidized dimer (P+) of the RC were measured during light excitation (induction) and relaxation (in the dark) for whole cells of photosynthetic bacterium Rhodobacter sphaeroides lacking cytochrome c_2 as natural electron donor to P+ (mutant cycA). The relationship between the fluorescence yield and P+ (fraction of closed RC) showed deviations from the standard Joliot-Lavergne-Trissl model: 1) the hyperbola is not symmetric and 2) exhibits hysteresis. These phenomena originate from the difference between the delays of fluorescence relative to P+ kinetics during induction and relaxation, and in structural terms from the non-random distribution of the closed RCs during induction. The experimental findings are supported by Monte Carlo simulations and by results from statistical physics based on random walk approximations of the excitation in the antenna. The applied mathematical treatment demonstrates the generalization of the standard theory and sets the stage for a more adequate description of the long-debated kinetics of fluorescence and of the delicate control and balance between efficient light harvest and photoprotection in photosynthetic organisms., Comment: 14 pages, 11 figures, Scientific Reports (in print)

We study the time-dependence of the local persistence probability during a non-stationary time evolution in the disordered contact process in $d=1,2$, and $3$ dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply in the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal, dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dependent local persistences is shown to be characterized by a universal limit distribution of effective persistence exponents. By a phenomenological approach of rare-region effects in the active phase, we obtain a non-universal algebraic decay of the average persistence for $d=1$, and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay holds to be valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time-dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations., Comment: 10 pages, 7 figures

Transfinite patches provide a simple and elegant solution to the problem of representing non-four-sided continuous surfaces, which are useful in a variety of applications, such as curve network based design. Real-time responsiveness is essential in this context, and thus reducing the computation cost is an important concern. The Midpoint Coons (MC) patch presented in this paper is a fusion of two previous transfinite schemes, combining the speed of one with the superior control mechanism of the other. This is achieved using a new constrained parameterization based on generalized barycentric coordinates and transfinite blending functions.

We prove that the group $C_p^4\times C_q$ is a DCI-group for distinct primes $p$ and $q$, that is, two Cayley digraphs over $C_p^4 \times C_q$ are isomorphic if and only if their connection sets are conjugate by a group automorphism., Comment: 20 pages

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with probability $p$ belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as $a(p) L^D$, where $a(p)$ is a non-universal function, to which there is a logarithmic correction term, $b(p)L^{D-1}\ln L$. In $1D$ the prefactor is given by $b(p)=\frac{c}{3} f(p)$, where $c$ is the central charge of the model and $f(p)$ is a universal function. In $2D$ the prefactor has a different functional form of $p$ below and above the percolation threshold., Comment: 9 pages, 9 figures

A Cayley graph of a group $H$ is a finite simple graph $\Gamma$ such that its automorphism group ${\rm Aut}(\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\Gamma)$, while a Haar graph of $H$ is a finite simple bipartite graph $\Sigma$ such that ${\rm Aut}(\Sigma)$ contains a subgroup isomorphic to $H$ acting semiregularly on $V(\Sigma)$ and the $H$-orbits are equal to the partite sets of $\Sigma$. It is well-known that every Haar graph of finite abelian groups is a Cayley graph. In this paper, we prove that every finite non-abelian group admits a non-Cayley Haar graph except the dihedral groups $D_6$, $D_8$, $D_{10}$, the quaternion group $Q_8$ and the group $Q_8\times\mathbb{Z}_2$. This answers an open problem proposed by Est\'elyi and Pisanski in 2016.

Motivation: Network visualizations of complex biological datasets usually result in 'hairball' images, which do not discriminate network modules. Results: We present the EntOptLayout Cytoscape plug-in based on a recently developed network representation theory. The plug-in provides an efficient visualization of network modules, which represent major protein complexes in protein-protein interaction and signalling networks. Importantly, the tool gives a quality score of the network visualization by calculating the information loss between the input data and the visual representation showing a 3- to 25-fold improvement over conventional methods. Availability and implementation: The plug-in (running on Windows, Linux, or Mac OS) and its tutorial (both in written and video forms) can be downloaded freely under the terms of the MIT license from: http://apps.cytoscape.org/apps/entoptlayout. Supplementary data are available at Bioinformatics online. Contact: csermely.peter@med.semmelweis-univ.hu

The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of ${\rm PG}(2,q)$ remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre-Korchm\'aros on Desargues configurations with perspective triangles inscribed in a conic.

A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring over the direct product of elementary abelian groups to be a $CI$-Schur ring. By using this condition we reprove in a short way known results on the $CI$-property for decomposable Schur rings over an elementary abelian group of rank at most $5$., Comment: 13 pages

The critical behavior of the random transverse-field Ising model in finite dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in $d=1,2$ and $3$ dimensions. At the critical point an algebraic decay of the form $\sim r^{-\eta_t}$ is found, with a decay exponent being approximately $\eta_t \approx 2+2d$. In $d=1$ the results are related to dimer-dimer correlations in the random AF XX-chain and have been tested by numerical calculations using free-fermionic techniques., Comment: 6 pages, 5 figures

Two permutations of $[n]=\{1,2 \ldots n\}$ are \textit{$k$-neighbor separated} if there are two elements that are neighbors in one of the permutations and that are separated by exactly $k-2$ other elements in the other permutation. Let the maximal number of pairwise $k$-neighbor separated permutations of $[n]$ be denoted by $P(n,k)$. In a previous paper, the authors have determined $P(n,3)$ for every $n$, answering a question of K\"orner, Messuti and Simonyi affirmatively. In this paper we prove that for every fixed positive integer $\ell $, $$P(n,2^\ell+1) = 2^{n-o(n)}. $$ We conjecture that for every fixed even $k$, $P(n,k)=2^{n-o(n)}$. We also show that this conjecture is asymptotically true in the following sense $$\lim_{k \rightarrow \infty} \lim_{n \rightarrow \infty} \sqrt[n]{P(n,k)}=2.$$ Finally, we show that for even $n$, $P(n,n)= 3n/2$.

A Cayley graph of a group $H$ is a finite simple graph $\Gamma$ such that ${\rm Aut}(\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\Gamma)$, while a Haar graph of $H$ is a finite simple bipartite graph $\Sigma$ such that ${\rm Aut}(\Sigma)$ contains a subgroup isomorphic to $H$ acting semiregularly on $V(\Sigma)$ and the $H$-orbits are equal to the bipartite sets of $\Sigma$. A Cayley graph is a Haar graph exactly when it is bipartite, but no simple condition is known for a Haar graph to be a Cayley graph. In this paper, we show that the groups $D_6, \, D_8, \, D_{10}$ and $Q_8$ are the only finite inner abelian groups all of whose Haar graphs are Cayley graphs (a group is called inner abelian if it is non-abelian, but all of its proper subgroups are abelian). As an application, it is also shown that every non-solvable group has a Haar graph which is not a Cayley graph., Comment: 17 pages

A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough. A graph is minimally $t$-tough if the toughness of the graph is $t$ and the deletion of any edge from the graph decreases the toughness. The complexity class DP is the set of all languages that can be expressed as the intersection of a language in NP and a language in coNP. In this paper, we prove that recognizing minimally $t$-tough graphs is DP-complete for any positive rational number $t$. We introduce a new notion called weighted toughness, which has a key role in our proof.

In this paper, we show that the group $\mathbb{Z}_p^5$ is a DCI-group for any odd prime $p,$ that is, two Cayley digraphs Cay$(\mathbb{Z}_p^5,S)$ and Cay$(\mathbb{Z}_p^5,T)$ are isomorphic if and only if $S=T^\varphi$ for some automorphism $\varphi$ of the group $\mathbb{Z}_p^5$.

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$, where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$. For $\kappa<1/2$, the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$, while for $\kappa \ge 1/2$, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments., Comment: 12 pages, 7 figures, Invited contribution to the Festschrift of John Cardy's 70th birthday

A planar point set of $n$ points is called {\em $\gamma$-dense} if the ratio of the largest and smallest distances among the points is at most $\gamma\sqrt{n}$. We construct a dense set of $n$ points in the plane with $ne^{\Omega\left({\sqrt{\log n}}\right)}$ halving lines. This improves the bound $\Omega(n\log n)$ of Edelsbrunner, Valtr and Welzl from 1997. Our construction can be generalized to higher dimensions, for any $d$ we construct a dense point set of $n$ points in $\mathbb{R}^d$ with $n^{d-1}e^{\Omega\left({\sqrt{\log n}}\right)}$ halving hyperplanes. Our lower bounds are asymptotically the same as the best known lower bounds for general point sets., Comment: 18 pages

Delivery of broadcast messages among vehicles for safety purposes, which is known as one of the key ingredients of Intelligent Transportation Systems (ITS), requires an efficient Medium Access Control (MAC) that provides low average delay and high reliability. To this end, a Geo-Location Based Access (GLOC) for vehicles has been proposed for Vehicle-to-Vehicle (V2V) communications, aiming at maximizing the distance of co-channel transmitters while preserving a low latency when accessing the resources. In this paper we analyze, with the aid of stochastic geometry, the delivery of periodic and non-periodic broadcast messages with GLOC, taking into account path loss and fading as well as the random locations of transmitting vehicles. Analytical results include the average interference, average Binary Rate (BR), capture probability, i.e., the probability of successful message transmission, and Energy Efficiency (EE). Mathematical analysis reveals interesting insights about the system performance, which are validated thought extensive Monte Carlo simulations. In particular, it is shown that the capture probability is an increasing function with exponential dependence with respect to the transmit power and it is demonstrated that an arbitrary high capture probability can be achieved, as long as the number of access resources is high enough. Finally, to facilitate the system-level design of GLOC, the optimum transmit power is derived, which leads to a maximal EE subject to a given constraint in the capture probability., Comment: 15 pages and 16 figures. This paper have been submitted for possible publication in IEEE Transactions on Vehicular Technology

Let $G$ be a fixed graph. Two paths of length $n-1$ on $n$ vertices (Hamiltonian paths) are $G$-different if there is a subgraph isomorphic to $G$ in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian paths is equal to the number of balanced bipartitions of the ground set, answering a question of K\"orner, Messuti and Simonyi., Comment: We slightly changed the introduction, added two more papers as references, and added a new short section which deals with the two related questions where Hamiltonian paths are replaced with arbitrary graphs and trees

A permutation of the point set of the affine space $AG(n,q)$ is called an integral automorphism if it preserves the integral distance defined among the points. In this paper, we complete the classification of the integral automorphisms of $AG(n,q)$ for $n\ge 3$.

This paper compares three candidate large-scale propagation path loss models for use over the entire microwave and millimeter-wave (mmWave) radio spectrum: the alpha-beta-gamma (ABG) model, the close-in (CI) free space reference distance model, and the CI model with a frequency-weighted path loss exponent (CIF). Each of these models have been recently studied for use in standards bodies such as 3GPP, and for use in the design of fifth generation (5G) wireless systems in urban macrocell, urban microcell, and indoor office and shopping mall scenarios. Here we compare the accuracy and sensitivity of these models using measured data from 30 propagation measurement datasets from 2 GHz to 73 GHz over distances ranging from 4 m to 1238 m. A series of sensitivity analyses of the three models show that the physically-based two-parameter CI model and three-parameter CIF model offer computational simplicity, have very similar goodness of fit (i.e., the shadow fading standard deviation), exhibit more stable model parameter behavior across frequencies and distances, and yield smaller prediction error in sensitivity testing across distances and frequencies, when compared to the four-parameter ABG model. Results show the CI model with a 1 m close-in reference distance is suitable for outdoor environments, while the CIF model is more appropriate for indoor modeling. The CI and CIF models are easily implemented in existing 3GPP models by making a very subtle modification -- by replacing a floating non-physically based constant with a frequency-dependent constant that represents free space path loss in the first meter of propagation., Comment: Open access available at: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7434656