Network Characterizations for Excluding Braess’s Paradox

Braess’s paradox exposes a counterintuitive phenomenon that when travelers selfishly choose their routes in a network, removing links can improve the overall network performance. Under the model of nonatomic selfish routing, we characterize the topologies of k-commodity undirected and directed networks in which Braess’s paradox never occurs. Our results strengthen Milchtaich’s series-parallel characterization (Milchtaich, Games Econom. Behav. 57(2), 321–346 (2006)) for the single-commodity undirected case.     

Braess’s Paradox for Flows over Time

We study the properties of Braess’s paradox in the context of the model of congestion games with flow over time introduced by Koch and Skutella. We compare them to the well known properties of Braess’s paradox for Wardrop’s model of games with static flows. We show that there are networks which do not admit Braess’s paradox in Wardrop’s model, but which admit it in the model with flow over time. Moreover, there is a topology that admits a much more severe Braess’s ratio for this model. Further, despite its symmetry for games with static flow, we show that Braess’s paradox is not symmetric for flows over time. We illustrate that there are network topologies which exhibit Braess’s paradox, but for which the transpose does not. Finally, we conjecture a necessary and sufficient condition of existence of Braess’s paradox in a network, and prove the condition of existence of the paradox either in the network or in its transpose.     

Valiant’s model and the cost of computing integers

Let (n) be the minimum number of arithmetic operations required to build the integer from the constants 1 and 2. A sequence x_n is said to be easy to compute if there exists a polynomial p such that for all It is natural to conjecture that sequences such as or n! are not easy to compute. In this paper we show that a proof of this conjecture for the first sequence would imply a superpolynomial lower bound for the arithmetic circuit size of the permanent polynomial. For the second sequence, a proof would imply a superpolynomial lower bound for the permanent or P PSPACE.     

The Interplay Between the Speaker’s and the Hearer’s Perspective

The neutralization of contrasts in form or meaning that is sometimes observed in language production and comprehension is at odds with the classical view that language is a systematic one-to-one pairing of forms and meanings. This special issue is concerned with patterns of forms and meanings in language. The papers in this special issue arose from a series of workshops that were organized to explore variants of bidirectional Optimality Theory and Game Theory as models of the interplay between the speaker’s and the hearer’s perspective.     

E-recruiting and fairness: the applicant’s point of view

More and more companies currently recruit online, partly because of cost savings and competitive pressure, and partly because it is the best way to reach their target group of applicants. In our study, applicants’ perceptions of procedural fairness were examined in e-recruiting contexts. Using an adapted form of the Social Process Questionnaire on Selection, we found that 1,373 participants’ expectations regarding fairness were mediocre and always lower than the perceived importance of five procedural fairness aspects. Based on an experimental manipulation, we showed that feedback was particularly important in online application procedures, whereas participation had smaller effects. Furthermore, participants tend to rate procedural fairness for offline application procedures as fairer than for online procedures although they reported generally positive experiences with online applications in the past. Based on our results, we discuss practical implications and limitations.     

Note on the Carleman’s inequality and Hardy’s inequality

In this article, using the properties of power mean and induction, new strengthened Carleman’s inequality and Hardy’s inequality are obtained. We also give an answer to the conjectures proposed by X. Yang in the literature Yang (2001) [5].     

Polylogarithms and the Asymptotic Formula for the Moments of Lebesgue’s Singular Function

Recall that Lebesgue’s singular function L(t) is defined as the unique solution to the equation L(t) = qL(2t) + pL(2t ? 1), where p, q > 0, q = 1 ? p, p ≠ q. The variables M _n = ∫₀¹t ⁿ dL(t), n = 0,1,… are called the moments of the function The principal result of this work is \({M_n} = {n^{{{\log }_2}p}}{e^{ - \tau (n)}}(1 + O({n^{ - 0.99}}))\), where the function τ(x) is periodic in log₂x with the period 1 and is given as \(\tau (x) = \frac{1}{2}1np + \Gamma '(1)lo{g_2}p + \frac{1}{{1n2}}\frac{\partial }{{\partial z}}L{i_z}( - \frac{q}{p}){|_{z = 1}} + \frac{1}{{1n2}}\sum\nolimits_{k \ne 0} {\Gamma ({z_k})L{i_{{z_k} + 1}}( - \frac{q}{p})} {x^{ - {z_k}}}\), \({z_k} = \frac{{2\pi ik}}{{1n2}}\), k ≠ 0. The proof is based on poissonization and the Mellin transform.     

Paradox Lost: The Evolution of Strategies in Selten’s Chain Store Game

The classical game theoretic resolutions to Selten’s Chain Store game are unsatisfactory; they either alter the game to avoid the paradox or struggle to organize the existing experimental data. This paper applies co-evolutionary algorithms to the Chain Store game and demonstrates that the resulting system’s dynamics are neither intuitively paradoxical nor contradicted by the existing experimental data. Specifically, some parameterizations of evolutionary algorithms promote genetic drift. Such drift can lead the system to transition among the game’s various Nash Equilibria. This has implications for policy makers as well as for computational modelers.     

Russell’s Structuralism and the Supposed Death of Computational Cognitive Science

John Searle believes that computational properties are purely formal and that consequently, computational properties are not intrinsic, empirically discoverable, nor causal; and therefore, that an entity’s having certain computational properties could not be sufficient for its having certain mental properties. To make his case, Searle’s employs an argument that had been used before him by Max Newman, against Russell’s structuralism; one that Russell himself considered fatal to his own position. This paper formulates a not-so-explored version of Searle’s problem with computational cognitive science, and refutes it by suggesting how our understanding of computation is far from implying the structuralism Searle vitally attributes to it. On the way, I formulate and argue for a thesis that strengthens Newman’s case against Russell’s structuralism, and thus raises the apparent risk for computational cognitive science too.

Small Space Analogues of Valiant’s Classes and the Limitations of Skew Formulas

In the uniform circuit model of computation, the width of a boolean circuit exactly characterizes the “space” complexity of the computed function. Looking for a similar relationship in Valiant’s algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space. In the uniform setting, we show that our definition coincides with that of VPSPACE at polynomial width. We introduce the class VL as an algebraic variant of deterministic log-space L; VL is a subclass of VP. Further, to define algebraic variants of non-deterministic space-bounded classes, we introduce the notion of “read-once” certificates for arithmetic circuits. We show that polynomial-size algebraic branching programs (an algebraic analog of NL) can be expressed as read-once exponential sums over polynomials in ${{\sf VL}, {\it i.e.}\quad{\sf VBP} \in \Sigma^R \cdot {\sf VL}}$ . Thus, read-once exponential sums can be viewed as a reasonable way of capturing space-bounded non-determinism. We also show that Σ ^R ·VBP = VBP, i.e. VBPs are stable under read-once exponential sums. Though the best upper bound we have for Σ ^R ·VL itself is VNP, we can obtain better upper bounds for width-bounded multiplicatively disjoint (md-) circuits. Without the width restriction, md- arithmetic circuits are known to capture all of VP. We show that read-once exponential sums over md- constant-width arithmetic circuits are within VP and that read-once exponential sums over md- polylog-width arithmetic circuits are within VQP. We also show that exponential sums of a skew formula cannot represent the determinant polynomial.     

Grover’s algorithm and the secant varieties

In this paper we investigate the entanglement nature of quantum states generated by Grover’s search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and auxiliary algebraic varieties built from the set of separable states. This new perspective enables us to propose qualitative interpretations of earlier numerical results obtained by M. Rossi et al. We also illustrate our purpose with a couple of examples investigated in details.     

An observer’s information dynamics: Acquisition of information and the origin of the cognitive dynamics

Conventional information science considers an information process, but traditionally uses the probability measure for random states and Shannon’s entropy as the uncertainty function of these states.This paper presents a new approach, based on an integral information measure of the random process.An entropy functional (EF) on the trajectories of the process accumulates and encodes the process’ inner connections between the information states.The application of a variation principle (VP) to the EF determines the process’ information path functional (IPF), whose extremal trajectories describe the informational dynamics of this process.Information dynamics with the VP invariant relations evaluate the information content of a random process, expose its information code and reveal a conserved (hidden) information, produced at an acquisition of the process information.By introducing both objective and subjective information observers, we consider the observers information cognitive dynamics and neurodynamics, based on the EF–IPF approach.The universal nature of information process’ dynamics and regularities, discovered in the information observers, have many applications not only in cognitive and intelligent systems, but also in different biological, social and economic systems.     

Modeling the influence of the Chelyabinsk meteorite’s bow shock wave on the Earth’s surface

The influence of the Chelyabinsk meteorite’s bow shock wave on the Earth’s surface is modeled. For solving the problem, a 3D statement is considered for its gas-dynamic and seismic parts. The determining equations of a gas-dynamic model and a seismic model are Euler equations with respect to the radiation heat exchange and the equations of linear elasticity theory, respectively. Two parts of the problem are matched by the direct mechanism of the disturbance transmission. A model seismic signal is compared with the real data. Modeling a seismic effect makes it possible to specify the estimate of the typical parameters of the phenomenon (height of the explosion, and the density and characteristic sizes of the meteorite).     

Modeling the patrol behavior of the Diacamma’s gamergate

The gamergate (generally called the “queen”) of the Diacamma sp. walks around in the nest and comes into contact with the workers. The gamergate informs the workers of its presence by physical contact. This behavior is called a “patrol.” In previous work, it was reported that the gamergate controls its patrolling time depending on the colony size. How does the gamergate know the colony size, and how does it control the patrolling time? In this article, we propose a simple dynamics to explain this behavior. We assume that the gamergate and the workers have internal states which interact by physical contacts. By numerical simulations, we confirm that the patrol time of the proposed model depends on the size of the colony.