Complexity of syntactical tree fragments of Independence-Friendly logic

A dichotomy result of Sevenster (2014) [29] completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain “Henkin” or “signalling” patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to be essentially first-order.In the present paper we develop the machinery which is needed in order to extend the results of Sevenster to non-prenex, regular IF sentences. This involves shifting attention from quantifier prefixes to a (rather general) class of syntactical tree prefixes.We partially classify the fragments of regular IF logic that are thus determined by syntactical trees; in particular, a) we identify four classes of tree prefixes that are neither signaling nor Henkin, and yet express NP-complete problems and other second-order concepts; and b) we give more general criteria for checking the first-orderness of an IF sentence.     

Lifting constructions of strongly regular Cayley graphs

We give two “lifting” constructions of strongly regular Cayley graphs. In the first construction we “lift” a cyclotomic strongly regular graph by using a subdifference set of the Singer difference sets. The second construction uses quadratic forms over finite fields and it is a common generalization of the construction of the affine polar graphs [7] and a construction of strongly regular Cayley graphs given in [15]. The two constructions are related in the following way: the second construction can be viewed as a recursive construction, and the strongly regular Cayley graphs obtained from the first construction can serve as starters for the second construction. We also obtain association schemes from the second construction.     

Nondegeneracy,from the prospect of wave-wave regular interactions of a gasdynamic type

A parallel is considered between Burnat's “algebraic” approach [restricted to a genuine nonlinearity] and Martin's “differential” approach regarding their contribution to describing some nondegenerate one-dimensional gasdynamic regular interaction solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

POPULATION‐LEVEL ANALYSIS AND VALIDATION OF AN INDIVIDUAL‐BASED CUTTHROAT TROUT MODEL

ABSTRACT. An individual‐based model of stream trout is analyzed by testing its ability to reproduce patterns of population‐level behavior observed in real trout: (1) “self‐thinning,” a negative power relation between weight and abundance; (2) a “critical period” of density‐dependent mortality in young‐of‐the‐year; (3) high and age‐specific inter‐annual variability in abundance; (4) density dependence in growth; and (5) fewer large trout when pool habitat is eliminated. The trout model successfully reproduced these patterns and was useful for evaluating their theoretical basis. The model analyses produced new explanations for some field observations and indicated that some patterns are less general than field studies indicate. The model did not reproduce field‐observed patterns of population variability by age class, discrepancies potentially explained by site differences, predation mortality being more stochastic than the model assumes, or uncertainty in the field study's age estimates.     

Interior hölder estimates for solutions of schrödinger equations and the regularity of nodal sets

Abstract

Motivated by the study of selfdual vortices in gauge field theory, we consider a class of Mean Field equations of Liouville-type on compact surfaces involving singular data assigned by Dirac measures supported at finitely many points (the so called vortex points). According to the applications, we need to describe the blow-up behavior of solution-sequences which concentrate exactly at the given vortex points. We provide accurate pointwise estimates for the profile of the bubbling sequences as well as “sup + inf” estimates for solutions. Those results extend previous work of Li [Li, Y. Y. (1999). Harnack type inequality: The method of moving planes. Comm. Math. Phys. 200:421–444] and Brezis et al. [Brezis, H., Li, Y. Shafrir, I. (1993). A sup + inf inequality for some nonlinear elliptic equations involving the exponential nonlinearities. J. Funct. Anal. 115: 344–358] relative to the “regular” case, namely in absence of singular sources.     

On exact solutions to the Kolmogorov–Feller equation

The integrodifferential Kolmogorov–Feller equation describing the stochastic dynamics of a system subjected to a regular “force” and a random external disturbance in the form of short pulses with random “amplitudes” and occurrence times is considered. The equation is written in differential form. A method for finding the regular force from a given stationary probability distribution is described. The method is illustrated by examples.     

Corrigendum to “Generalized periodicity and primitivity for words”

We correct a mistake in the paper “Generalized periodicity and primitivity for words” [4] and justify the existence of regular languages all of whose roots are not even context‐sensitive. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields

The equilibrium measure in the presence of an external field plays a role in a number of areas in analysis, for example, in random matrix theory: The limiting mean density of eigenvalues is precisely the density of the equilibrium measure. Typical behavior for the equilibrium measure is:

• 1 it is positive on the interior of a finite number of intervals,
• 2 it vanishes like a square root at endpoints, and
• 3 outside the support, there is strict inequality in the Euler‐Lagrange variational conditions.

If these conditions hold, then the limiting local eigenvalue statistics is loosely described by a “bulk,” in which there is universal behavior involving the sine kernel, and “edge effects,” in which there is a universal behavior involving the Airy kernel. Through techniques from potential theory and integrable systems, we show that this “regular” behavior is generic for equilibrium measures associated with real analytic external fields. In particular, we show that for any one‐parameter family of external fields V/c, the equilibrium measure exhibits this regular behavior except for an at most countable number of values of c. We discuss applications of our results to random matrices, orthogonal polynomials, and integrable systems. © 2000 John Wiley & Sons, Inc.     

Using chaos to reduce oscillations: Experimental results

Chaotic dynamic systems are usually controlled in a way, which allows the replacement of chaotic behavior by the desired periodic motion. We give the example in which an originally regular (periodic) system is controlled in such a way as to make it chaotic. This approach based on the idea of dynamical absorber allows the significant reduction of the amplitude of the oscillations in the neighborhood of the resonance. We present experimental results, which confirm our previous numerical studies [D?browski A, Kapitaniak T. Using chaos to reduce oscillations. Nonlinear Phenomen Complex Syst 2001;4(2):206–11].     

Reciprocal inhibitory coupling: Measure and control of chaos on a biophysically motivated model of bursting

Bursting activity is an interesting feature of the temporal organization in many cell firing patterns. This complex behavior is characterized by clusters of spikes (action potentials) interspersed with phases of quiescence. As shown in experimental recordings, concerning the electrical activity of real neurons, the analysis of bursting models reveals not only patterned periodic activity but also irregular behavior [1], [2]. The interpretation of experimental results, particularly the study of the influence of coupling on chaotic bursting oscillations, is of great interest from physiological and physical perspectives. The inability to predict the behavior of dynamical systems in presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we focus our attention on a specific class of biophysically motivated maps, proposed in the literature to describe the chaotic activity of spiking–bursting cells [Cazelles B, Courbage M, Rabinovich M. Anti-phase regularization of coupled chaotic maps modelling bursting neurons. Europhys Lett 2001;56:504–9]. More precisely, we study a map that reproduces the behavior of a single cell and a map used to examine the role of reciprocal inhibitory coupling, specially on two symmetrically coupled bursting neurons. Firstly, using results of symbolic dynamics, we characterize the topological entropy associated to the maps, which allows us to quantify and to distinguish different chaotic regimes. In particular, we exhibit numerical results about the effect of the coupling strength on the variation of the topological entropy. Finally, we show that complicated behavior arising from the chaotic coupled maps can be controlled, without changing of its original properties, and turned into a desired attracting time periodic motion (a regular cycle). The control is illustrated by an application of a feedback control technique developed by Romeiras et al. [Romeiras FJ, Grebogi C, Ott E, Dayawansa WP. Controlling chaotic dynamical systems. Physica D 1992;58:165–92]. This work provides an illustration of how our understanding of chaotic bursting models can be enhanced by the theory of dynamical systems.     

Hospital efficiency with risk adjusted mortality as undesirable output: the Turkish case

We analyze the operational performance of 202 Turkish rural general hospitals. To help improve performance on both input and output space, we adopt a directional distance approach. We treat a mortality based measure as a “needs indicator”. We derive pure technical, scale and output congestion inefficiency measures and show how they vary across size classes. We show that “reducing mortality” involves sacrificing some good outputs. This is a trade off that holds at the potential output level. Second stage regressions of the inefficiency scores against hospital and rural district level variables, pinpoint critical areas for performance improvement. In particular we show the relative scarcity of nurses is linked to output congestion.     

On the Chebyshev spectral continuous time approximation for constant and periodic delay differential equations

In this paper, the approximation technique proposed in Breda et al. (2005) [1] for converting a linear system of constant-coefficient delay differential equations (DDEs) into a system of ordinary differential equations (ODEs) using pseudospectral differencing is extended to linear and nonlinear systems of DDEs with time-periodic coefficients. The Chebyshev spectral continuous time approximation (ChSCTA) technique is used to study the stability of first and second-order constant coefficient DDEs, a delayed system with a cubic nonlinearity and parametric sinusoidal excitation, the delayed Mathieu’s equation, and delayed systems with two fixed delays. In all the examples, the stability and time response obtained from ChSCTA show good agreement with either analytical results, or the results obtained before by other reliable approximation methods. The “spectral accuracy” convergence behavior of Chebyshev spectral collocation shown in Trefethen (2000) [2] which the proposed technique possesses is compared to the convergence properties of finite difference-based continuous time approximation for constant-coefficient DDEs proposed recently in Sun (2009) [3] and Sun and Song (2009) [4].     

Numerical Assessment of Stabilization Techniques for Coupled Poro-plastic Analysis using Low-Order Finite Elements

For the numerical modeling of geomaterials in general, and soft, water saturated soils in particular, the nonlinear constitutive behavior of the skeleton and its strong coupling with the pore fluid must be considered. In the limit of zero compressibility of water and soil grains and very low permeability (which correspond to the classical “undrained” assumption in soil mechanics), the functions used to interpolate displacements and pressures must fulfill either the Ladyženskaja-Babuška-Brezzi inf-sup condition [1] or the much simpler patch test proposed by Zienkiewicz and Taylor. These requirements exclude the use of elements with equal order of linear interpolation for pressures and displacements, for which spurious oscillations may appear. Low-order elements with linear approximation of displacements and pressure variables may be used if stabilization techniques are employed. The work is concerned with the numerical assessment and investigation of several stabilization techniques and their application to strain localization problems in coupled poro-plastic analyses of soft, saturated soils [2,3]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On left regular and intra-regular ordered semigroups

We study the decomposition of left regular ordered semigroups into left regular components and the decomposition of intra-regular ordered semigroups into simple or intra-regular components, adding some additional information to the results considered in [KEHAYOPULU, N.: On left regular ordered semigroups, Math. Japon. 35 (1990), 1057–1060] and [KEHAYOPULU, N.: On intra-regular ordered semigroups, Semigroup Forum 46 (1993), 271–278]. We prove that an ordered semigroup S is left regular if and only if it is a semilattice (or a complete semilattice) of left regular semigroups, equivalently, it is a union of left regular subsemigroups of S. Moreover, S is left regular if and only if it is a union of pairwise disjoint left regular subsemigroups of S. The right analog also holds. The same result is true if we replace the words “left regular” by “intraregular”. Moreover, an ordered semigroup is intra-regular if and only if it is a semilattice (or a complete semilattice) of simple semigroups. On the other hand, if an ordered semigroup is a semilattice (or a complete semilattice) of left simple semigroups, then it is left regular, but the converse statement does not hold in general. Illustrative examples are given.     

A dynamical approach to logical decisions

We propose a first approximation to the modeling of cognitive decisions based on the theory of associative memories. The basic structure are the matrix memories of Anderson-Kohonen adapted to include the modulation of associations via tensorial preprocessing of inputs. This view admits an easy implementation of logical operations as matrix operators. From this “vectorial logic” springs a variety of models for fuzzy decision processes. Degrees of fuzziness are introduced at two different levels: (a) by the operators of modal logic, and (b) by using logical variables as vectors with projections inside the interval [0, 1]. The outcomes of this vectorial logic can be projected onto unit vectors yielding scalar difference equations. As examples we study the dynamics of contradictory self-referential systems and processes leading to competition between options. These models exhibit a variety of dynamical patterns that include stable steady states, oscillations, and deterministic chaos. © 1997 John Wiley & Sons, Inc.     

The capacities of certain special channels with arbitrarily varying channel probability functions

In [5] Ahlswede and Wolfowitz have obtained the capacities of a.v.ch. with binary output in a number of cases, essentially with the aid of a lemma which relates the capacity of the a.v.ch. to that of a suitable (“underlying”) d.m.c. A generalization of this lemma to a special kind of a.v.ch. with output alphabet b>2, has been given by Ahlswede (Lemma 1 of [1]) and used in [1] and [2] to prove the existence of the weak capacities of various channels under different conditions. We give a detailed proof of a weakened version of Ahlswede's lemma and show, in passing, that his lemma is incorrect. We then define certain special types of a.v.ch and, on the basis of the detailed analysis given by us earlier, we prove lemmas of a similar type for these a.v.ch. We are thus able to extend certain results given for binary output a.v.ch. in [4] and [5] to these special a.v.ch. for which b>2.     

A backward–forward regularization of the Perona–Malik equation

It is shown that the Perona–Malik equation (PME) admits a natural regularization by forward–backward diffusions possessing better analytical properties than PME itself. Well-posedness of the regularizing problem along with a complete understanding of its long time behavior can be obtained by resorting to weak Young measure valued solutions in the spirit of Kinderlehrer and Pedregal (1992) [1] and Demoulini (1996) [2]. Solutions are unique (to an extent to be specified) but can exhibit “micro-oscillations” (in the sense of minimizing sequences and in the spirit of material science) between “preferred” gradient states. In the limit of vanishing regularization, the preferred gradients have size 0 or ∞ thus explaining the well-known phenomenon of staircasing. The theoretical results do completely confirm and/or predict numerical observations concerning the generic behavior of solutions.     

Global weak solutions and asymptotics of a singular PDE-ODE Chemotaxis system with discontinuous data

This paper is concerned with the well-posedness and large-time behavior of a two-dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis. We first transform the system via a Cole-Hopf type transformation into a parabolic-hyperbolic system and then show that the solution to the transformed system converges to a constant equilibrium state as time tends to infinity. Finally we reverse the Cole-Hopf transformation and obtain the relevant results for the pre-transformed PDE-ODE hybrid system.In contrast to the existing related results, where continuous initial data is imposed, we are able to prove the asymptotic stability for discontinuous initial data with large oscillations. The key ingredient in our proof is the use of the so-called "effective viscous flux", which enables us to obtain the desired energy estimates and regularity. The technique of the "effective viscous flux" turns out to be a very useful tool to study chemotaxis systems with initial data having low regularity and was rarely(if not) used in the literature for chemotaxis models.     

Complements,mollifiers and the propensity to disrupt

Gately [1974] andLittlechild/Vaidya [1976] defined and studied ratio measures of “disruption propensity” of coalitions in ann-person game. We define and study new incremental measures giving rise to a wide variety of “disruption solution” concepts free of various ratio defects and affording advantages of analysis and acceptability in terms of solution specifications. Various “mollifier” and “homomollifier” solution concepts are characterized which appear to be of promising utility.     

Never say “not”: Impact of negative wording in probability phrases on imprecise probability judgments

Effective translations between numerical and verbal representations of uncertainty are a concern shared by researchers in cognitive science and psychology, with applications to real-world risk management and decision support systems. While there is a substantial literature on such translations for point-wise probabilities, this paper contributes to the scanty literature on imprecise probability translations. Reanalysis of Budescu et al.’s [1] data on numerical interpretations of the Intergovernmental Panel on Climate Change [2] fourth report’s verbal probability expressions (PEs) revealed that negative wording has deleterious effects on lay judgements. Budescu et al. asked participants to interpret PEs in IPCC report sentences, by asking them to provide lower, “best” and upper estimates of the probabilities that they thought the authors intended. There were four experimental conditions, determining whether participants were given any numerical guidelines for translating the PEs into numbers.The first analysis focuses on twelve sentences in Budescu et al. that used the PE “very likely,” “likely,” “unlikely,” or “very unlikely”. A mixed beta regression modelling the lower, “best” and upper estimates revealed a less regressive mean and less dispersion for positive than for negative wording in all three estimates, for both the “very likely” and “likely” sentence sets. The Budescu et al. data also included a task asking for context-free translations of these PEs, and a similar pattern of results was found for that task. Negative wording therefore resulted in more regressive estimates and less consensus regardless of experimental condition.The second analysis focuses on two statements that were positive–negative duals. Appropriate pairs of responses were assessed for conjugacy and additivity. A large majority of respondents were appropriately super- and sub-additive in their lower and upper probability estimates. A mixed beta regression model of these three variables revealed that respondents were suprisingly close to obeying the conjugacy relationships for lower and upper probabilities.