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Topological bifurcations in a model society of reasonable contrarians

Physical Review E 2013年第6期88卷 062914-062914页

作者： Franco Bagnoli Raúl Rechtman []Dipartimento di Fisica e Astronomia Università di Firenze Via G. Sansone 1 50017 Sesto Fiorentino (FI) Italy and INFN sez. Firenze Italy

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

关键词： SOCIAL norms SECURITIES markets CELLULAR automata ANTIFERROMAGNETIC materials deterministic algorithms PSYCHOLOGICAL aspects SOCIAL aspects

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Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation

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JOURNAL OF MATHEMATICAL PHYSICS 2017年第3期58卷 033301-033301页

作者： Domingo, Dario d'Onofrio, Alberto Flandoli, Franco Univ Leeds Sch Math Leeds W Yorkshire England Univ Pisa Dept Math Pisa Italy Int Prevent Res Inst Lyon France

An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show that the aforementioned procedure can be fallacious and lead to incorrect results. We indeed provide a counter-example concerning one of the most employed bounded noises, hereafter called Tsallis-Stariolo-Borland (TSB) noise, which admits the well known Tsallis q-statistics as stationary density. In fact, we show that for negative values of the Tsallis parameter q (corresponding to sufficiently large diffusion coefficient of the stochastic force), the motion resulting from the overdamped approximation is unbounded. We then investigate the cause of the failure of Kramers first type approximation, and we formally show that the solutions of the full Newtonian non-approximated model are bounded, following the physical intuition. Finally, we provide a new family of bounded noises extending the TSB noise, the boundedness of whose solutions we formally show. Published by AIP Publishing.

关键词： DIFFUSION coefficients STOCHASTIC approximation BIOPHYSICS deterministic algorithms GAUSSIAN distribution

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Stochastic dynamics on slow manifolds

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2013年第29期46卷 295002-295002页

作者： Constable, George W. A. McKane, Alan J. Rogers, Tim Univ Manchester Sch Phys & Astron Manchester M13 9PL Lancs England Univ Bath Ctr Networks & Collect Behav Dept Math Sci Bath BA2 7AY Avon England

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable simplification. In this paper we demonstrate how the same basic methodology may also be applied to stochastic dynamical systems, by examining the behaviour of trajectories conditioned on the event that they do not depart the slow manifold. We apply the method to two models: one from ecology and one from epidemiology, achieving a reduction in model dimension and illustrating the high quality of the analytical approximations.

关键词： MANIFOLDS (Mathematics) RESEARCH deterministic algorithms EPIDEMIOLOGY STOCHASTIC analysis DYNAMICAL systems

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Weak multiplexing induces coherence resonance

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CHAOS 2018年第5期28卷 051104-051104页

作者： Semenova, Nadezhda Zakharova, Anna Saratov NG Chernyshevskii State Univ Dept Phys Astrakhanskaya Str 83 Saratov 410012 Russia Tech Univ Berlin Inst Theoret Phys Hardenbergstr 36 D-10623 Berlin Germany

Using the model of a FitzHugh-Nagumo system in the excitable regime, we study the impact of multiplexing on coherence resonance in a two-layer network. We show that multiplexing allows for the control of the noise-induced dynamics. In particular, we find that multiplexing induces coherence resonance in networks that do not demonstrate this phenomenon in isolation. Examples are provided by deterministic networks and networks where the strength of interaction between the elements is not optimal for coherence resonance. In both cases, we show that the control strategy based on multiplexing can be successfully applied even for weak coupling between the layers. Moreover, for the case of deterministic networks, we obtain a counter-intuitive result: the multiplex-induced coherence resonance in the layer which is deterministic in isolation manifests itself even more strongly than that in the noisy layer.

关键词： MULTIPLEXING (Telecommunication) DATA transmission systems COHERENT states RESONANCE deterministic algorithms

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On the Impact of Fading and Interference on Contention-based Geographic Routing in VANETs

On the Impact of Fading and Interference on Contention-based...

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IEEE Vehicular Technology Conference

作者： Thomas Paulin Stefan Ruehrup FTW - Telecommunications Research Center Vienna Austria

ISBN: (纸本)9781479980925

Geographic routing is a method to distribute information in vehicular ad hoc networks over multiple hops. The basic principle is to forward a message to a neighboring station in the network that is closest to the destination area. In contention-based algorithms this next neighbor selection is done in a distributed way, where potential next hop candidates delay their forwarding attempt in a way that the candidate with the largest progress to the destination forwards the message first;other candidates cancel their scheduled retransmissions then. This elegant principle unfortunately depends on a consistent timing and the absence of transmission failures, which cannot be expected in vehicular networks based on IEEE 802.11. This paper illustrates how the re-ordering of channel access attempts through the 802.11 MAC layer and the transmission errors caused by frame collisions impact delivery rate and communication overhead. A counter-intuitive finding is that the delivery rate of contention-based forwarding increases under fading conditions (i.e. higher frame errors), but at the cost of packet duplication and thus higher overhead. Without fading, duplication is low, but more end-to-end delivery failures occur. In this paper, we explain the reasons for this behaviour analytically and illustrate it in simulations. Furthermore, we propose a randomized contention-based routing algorithm that balances the trade-off between high end-to-end delivery and low overhead better than the deterministic algorithm and shows a significant performance increase independent of whether fading or frame collisions are present.

关键词： Impact Fading Interference fading color interference V2V destination deterministic algorithms MAC layer Obstetric Delivery

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Towards power-sensitive communication on a multiple-access channel

Towards power-sensitive communication on a multiple-access c...

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IEEE International Conference on Distributed Computing Systems

作者： Gianluca De Marco Dariusz R. Kowalski Dipartimento di Informatica e Applicazioni Universita di Salerno University of Liverpool

ISBN: (纸本)9781424472611;9780769540597

We are given n stations of which k are active, while the remaining n - k are asleep. The active stations communicate via a multiple-access channel. If a subset Q of active stations transmits in the same round, all active stations can recognize from the signal strength how many stations have transmitted (i.e., they learn the size of set Q), even though they may not be able to decode the contents of transmitted messages. The goal is to let each active station to learn about the set of all active stations. It is well known that Θ(klog_(k+1)n) rounds are enough, even for non-adaptive deterministic algorithms. A natural interesting generalization arises when we are required to identify a subset of m ≤ k active stations. We show that while for randomized or for adaptive deterministic algorithms _(m log_(m+1) n) rounds are sufficient, the non-adaptive deterministic counterpart still requires Θ(klog_(k+1)n) rounds;therefore, finding any subset of active stations is not easier than finding all of them by a non-adaptive deterministic algorithm. We prove our results in the more general framework of combinatorial search theory, where the problem of identifying active stations on a multiple-access channel can be viewed as a variant of the well-known counterfeit coin problem.

关键词： Multiple-access channel Distributed learning Randomized algorithms Combinatorial search theory Multiple Access Channel randomized algorithms STATIONS multiple access Distance learning deterministic algorithms Active Access Channels Subset Signal Intensity Rounding off

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A stochastic hybrid algorithm for robust global almost sure synchronization on the circle: all-to-all communication

A stochastic hybrid algorithm for robust global almost sure ...

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IEEE Annual Conference on Decision and Control

作者： A. Subbaraman M. Hartman A.R. Teel Electrical and Computer Engineering Department University of California Santa Barbara CA 93106-9560

ISBN: (纸本)9781467357159

A stochastic hybrid algorithm for guaranteeing global almost sure synchronization of a finite number of agents evolving on the circle is presented. We assume all-to-all communication where every agent has access to the same aggregate quantity corresponding to an average of the position of the agents. The lack of robustness of deterministic algorithms to adversaries and slow convergence properties of stochastic gossip algorithms are overcome by using a stochastic hybrid feedback.

关键词： Circles Stochastic deterministic algorithms Agents Communication Research

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Faster Fully Dynamic Matchings with Small Approximation Ratios 16

Faster Fully Dynamic Matchings with Small Approximation Rati...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Aaron Bernstein Cliff Stein Department of Computer Science Columbia University Department of IEOR and Computer Science Columbia University

ISBN: (纸本)9781510819672

Maximum cardinality matching is a fundamental algorithmic problem with many algorithms and applications. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for dynamic matching (in general n-vertex m-edge graphs) fall into two groups: there are fast (mostly randomized) algorithms that achieve a 2-approximation or worse, and there are slow algorithms with Ω({the square root of}m) update time that achieve a better-than-2 approximation. Thus the obvious question is whether we can design an algorithm that achieves a tradeoff between these two: a o({the square root of}m) update time and a better-than-2 approximation simultaneously. We answer this question in the affirmative. Previously, such bounds were only known for the special case of bipartite graphs. Our main result is a fully dynamic deterministic algorithm that maintains a (3/2 + ε)-approximation in amortized update time O(m~(1/4)ε~(-2.5)). In addition to achieving the trade-off described above, our algorithm manages to be polynomially faster than all existing deterministic algorithms (excluding an existing log n-approximation of Onak and Rubinfeld), while still maintaining a better-than-2 approximation. We also give stronger results for graphs whose arboricity is at most α. We show how to maintain a (1 + ε)-approximate fractional matching or a (3/2+ε)-approximate integral matching in worst-case time O(α(α + log n)) for constant ε. When the arboricity is constant, this bound is O(log n) and when the arboricity is polylogarithmic the update time is also polylogarithmic. Previous results for small arboricity non-bipartite graphs could only maintain a maximal matching (2-approximation). We maintain the approximate matching without explicitly using augmenting paths. We define an intermediate graph, called an EDCS and show that the EDCS H contains a large matching, and show how to maintain an EDCS in G. The EDCS was used in previ

关键词： Bipartite graph refresh time deterministic algorithms algorithms approximate match TWO-COMPONENT dynamic matching Hydrogen

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Beating Brute Force for Systems of Polynomial Equations over Finite Fields 17

Beating Brute Force for Systems of Polynomial Equations over...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Daniel Lokshtanov Ramamohan Paturi Suguru Tamaki Ryan Williams Huacheng Yu University of Bergen University of California San Diego Kyoto University Stanford University

ISBN: (纸本)9781510836358

We consider the problem of solving systems of multivariate polynomial equations of degree k over a finite field. For every integer k ≥ 2 and finite field F_q where q = p~d for a prime p, we give, to the best of our knowledge, the first algorithms that achieve an exponential speedup over the brute force O(q~n) time algorithm in the worst case. We present two algorithms, a randomized algorithm with running time q~(n+o(n)) · q~(-n/O(k)) time if q ≤ 2~(4ekd), and q~(n+o(n))·(log q/dek)~(-dn) otherwise, where e = 2.718... is Napier's constant, and a deterministic algorithm for counting solutions with running time q~(n+o(n))·q~(-n/O(kq~(6/7d))). For the important special case of quadratic equations in F_2, our randomized algorithm has running time O(2~(0.8765n)). For systems over F_2 we also consider the case where the input polynomials do not have bounded degree, but instead can be efficiently represented as a ΣΠΣ circuit, i.e., a sum of products of sums of variables. For this case we present a deterministic algorithm running in time 2~(n-δn) for δ = 1/O(log(s/n)) for instances with s product gates in total and n variables. Our algorithms adapt several techniques recently developed via the polynomial method from circuit complexity. The algorithm for systems of ΣΠΣ polynomials also introduces a new degree reduction method that takes an instance of the problem and outputs a subexponential-sized set of instances, in such a way that feasibility is preserved and every polynomial among the output instances has degree O(log(s/n)).

关键词： Galois fields deterministic algorithms randomized algorithms Polynomial Runtime algorithms circuit complexity Beating

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Polylogarithmic Bounds on the Competitiveness of Min-cost Perfect Matching with Delays 17

Polylogarithmic Bounds on the Competitiveness of Min-cost Pe...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Yossi Azar Ashish Chiplunkar Haim Kaplan Tel Aviv University

ISBN: (纸本)9781510836358

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) recently introduced by Emek et al, (STOC 2016). This problem is defined on an underlying n-point metric space. An adversary presents real-time requests online at points of the metric space, and the algorithm is required to match them, possibly after keeping them waiting for some time. The cost incurred is the sum of the distances between matched pairs of requests (the connection cost), and the sum of the waiting times of the requests (the delay cost). We prove the first logarithmic upper bound and the first polylogarithmic lower bound on the randomized competitive ratio of this problem. We present an algorithm with a competitive ratio of O(log n), which improves the upper bound of O(log~2 n + log Δ) of Emek et al, by removing the dependence on Δ, the aspect ratio of the metric space (which can be unbounded as a function of n). The core of our algorithm is a deterministic algorithm for MPMD on metrics induced by edge-weighted trees of height h, whose cost is guaranteed to be at most O(1) times the connection cost plus O(h) times the delay cost of every feasible solution. The reduction from MPMD on arbitrary metrics to MPMD on trees is achieved using the result on embedding n-point metric spaces into distributions over weighted hierarchically separated trees of height O(log n), with distortion O(log n). We also prove a lower bound of Ω({the square root of}(log n)) on the competitive ratio of any randomized algorithm. This is the first lower bound which increases with n, and is attained on the metric of n equally spaced points on a line.

关键词： metric space Competitiveness delay Costs Metronidazole algorithms Lower bound deterministic algorithms randomized algorithms Perfect Matched pairs

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