Equiparadoxicality of Yablo’s Paradox and the Liar

It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition.     

Antonelli’s Dome for San Gaudenzio: Geometry and Statics

In this brief note the authors describe the studies undertaken to date regarding the dome of the Basilica of San Gaudenzio in Novara designed by Alessandro Antonelli, with particular emphasis on the geometry and statics of the external dome. Following a brief summary of the events and vicissitudes attendant on the construction of the dome, the structure will be examined from the point of view of the geometry, the construction techniques, and the materials used, in order to clarify the static behaviour and the stability of the whole set of structural and constructive elements of which the dome is composed. These studies have allowed us to obtain the necessary information for evaluating the complex and ambitious structural achievement of a significant element of Antonelli’s basilica.     

The Hidden Order of Hadrian’s Villa, and the Order of Modern Architecture

The casual violence with which the various parts of the second-century Villa of Hadrian crash into each other seems to belie any possibility of a rational plan, although an overall master plan seems a necessity. Amazingly, in the twentieth century, Le Corbusier extolled Hadrian’s Villa as the archetype of great planning. This paper will describe the clear, mathematically ordered process by which the Villa was planned, and the compositional principles of its design will be shown to be exactly those which underlie the theories of Corbusier, 1800 years later.     

Detection of the non-topology preservation of Ma and Sonka’s algorithm,by the use of P-simple points

In 1996, Ma and Sonka proposed a thinning algorithm which yields curve skeletons for 3D binary images [C. Ma, M. Sonka, A fully parallel 3D thinning algorithm and its applications, Comput. Vis. Image Underst. 64 (3) (1996) 420–433]. This algorithm is one of the most referred thinning algorithms in the context of digital topology: either by its use in medical applications or for comparisons with other thinning algorithms.In 2007, Wang and Basu [T. Wang, A. Basu, A note on ‘a fully parallel 3D thinning algorithm and its applications’, Pattern Recognit. Lett. 28 (4) (2007) 501–506] wrote a paper in which they claim that Ma and Sonka’s 3D thinning algorithm does not preserve topology. As they highlight in their paper, a counter-example was given in 2001, in Lohou’s thesis [C. Lohou, Contribution à l’analyse topologique des images: étude d’algorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrète. Ph.D. thesis, University of Marne-la-Vallée, France, 2001].In this paper, it is shown how P-simple points have guided the author towards a proof that Ma and Sonka’s algorithm does not always preserve topology. Moreover, the reasoning being very general, it could be reused for such a purpose, i.e., to simplify the proof on the non-topology preservation.     

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.     

Network Externalities,Incumbent’s Competitive Advantage and the Degree of Openness of Software Start-Ups

This paper proposes a formal model that analyzes the degree of openness chosen by start-ups when entering the software industry. In line with the literature, we label as degree of openness the extent to which software start-ups mix open source (OS) and proprietary solutions in the portfolio of software products they offer. We relate the choice of the degree of openness to two key characteristics of the market segments in which software start-ups operate: the strength of the network externalities and the competitive advantage of the incumbent. Specifically, by modelling (price) competition between an incumbent and an entrant in two ways, i.e., the entrant is price-setter or price-taker, we derive the necessary condition(s) in terms of the strength of network externalities for observing the adoption of a business model that comprises the offering of both proprietary and OS solutions by the entrant (i.e., hybrid business model). Then, we highlight that, if a hybrid business model is the choice, the degree of openness chosen in equilibrium increases along with both the strength of the network externalities and the competitive advantage of the incumbent. This result holds indifferently whether the software start-up is modelled as a price-setter or a price-taker. An empirical test run on a sample of European start-ups in the software industry supports these theoretical predictions.     

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.     

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).