Credit market dynamics: a cobweb model

Starting from a recent model developed by Dieci and Westerhoff (Appl Math Comput 215:2011–2023, 2009; J Econ Behav Organ 75(3):461–481, 2010) enriching the classic cobweb framework based on the findings of Brock and Hommes (Econometrica 65:1059–1095, 1997; J Econ Dynam Control 22:1235–1274, 1998), an original model is set up to analyse the interactions among two types of credit markets considered from the aggregate demand side view point. The proposed model is an aggregate model for unobserved Financial Institutions which are assumed to supply credit on competitive markets and competition is due to the interest rates (i.e. prices) with respect to the corresponding contracts’ demand. Moreover these Financial Institutions can put contracts on the credit market switching over time on different types of contracts depending on expected profit differentials. Among the main characteristics of this model, the number of clients involved in the two credit markets changes over time. At any time, the density of contracts is assumed to maximize the entropy of the economic system under some constraints concerning aggregate profits where the contract profitability is defined as a function of the spread between the average price of the contracts and a measure of production costs. With reference to some model calibrations, the dynamic behaviours and the reactions of the model are investigated through the study of three shock scenarios. The promising obtained results will address further investigations to apply the proposed model to a real data base of information on Financial Institutions in Italy since 1997 to catch the dynamics of fixed and adjustable interest rate mortgages markets.     

Bifurcation in Perturbation Analysis:Calvo Pricing Examples

In recent macro models with staggered price and wage settings, the presence of variables such as relative price and wage dispersion is prevalent, which leads to the source of bifurcations. In this paper, we illustrate how to detect the existence of a bifurcation in stylized macroeconomic models with Calvo (J Monet Econ 12(3):383–398, 1983) pricing. Following the general approach of Judd (Numerical methods in economics, 1998), we employ l’Hospital’s rule to characterize the first-order dynamics of relative price distortion in terms of its higher-order derivatives. We also show that, as in the usual practice in the literature, the bifurcation can be eliminated through renormalization of model variables. Furthermore, we demonstrate that the second-order approximate solutions under this renormalization and under bifurcations can differ significantly.     

A Closed-Form Solution to Stollery’s Problem with Damage in Utility

Stollery (Can J Econ 31(3):730–742, 1998) studied a polluting oil-extracting economy governed by a constant utility criterion. The pollution, resulted from oil use, negatively affected production and utility. Stollery provided a closed-form solution for the case where only the production function was affected by the damage. This paper offers a closed-form solution to a non-trivial example of this economy with damage in the utility function. The solution is used for the analysis of uncertainties in resource policy caused by uncertainties in reserve estimate and in the intensity of the damage.     

The Steiner Ratio Conjecture of Gilbert-Pollak May Still Be Open

We offer evidence in the disproof of the continuity of the length of minimum inner spanning trees with respect to a parameter vector having a zero component. The continuity property is the key step of the proof of the conjecture in Du and Hwang (Proc. Nat. Acad. Sci. U.S.A. 87:9464–9466, 1990; Algorithmica 7(1):121–135, 1992). Therefore the Steiner ratio conjecture proposed by Gilbert-Pollak (SIAM J. Appl. Math. 16(1):1–29, 1968) has not been proved yet. The Steiner ratio of a round sphere has been discussed in Rubinstein and Weng (J. Comb. Optim. 1:67–78, 1997) by assuming the validity of the conjecture on a Euclidean plane in Du and Hwang (Proc. Nat. Acad. Sci. U.S.A. 87:9464–9466, 1990; Algorithmica 7(1):121–135, 1992). Hence the results in Rubinstein and Weng (J. Comb. Optim. 1:67–78, 1997) have not been proved yet.     

Orientation contrast sensitive cells in primate V1 <Emphasis Type="Italic">a computational model</Emphasis>

Many cells in the primary visual cortex respond differently when a stimulus is placed outside their classical receptive field (CRF) compared to the stimulus within the CRF alone, permitting integration of information at early levels in the visual processing stream that may play a key role in intermediate-level visual tasks, such a perceptual pop-out [Knierim JJ, van Essen DC (1992) J Neurophysiol 67(5):961–980; Nothdurft HC, Gallant JL, Essen DCV (1999) Visual Neurosci 16:15–34], contextual modulation [Levitt JB, Lund JS (1997) Nature 387:73–76; Das A, Gilbert CD (1999) Nature 399:655–661; Dragoi V, Sur M (2000) J Neurophysiol 83:1019–1030], and junction detection [Sillito AM, Grieve KL, Jones HE, Cudiero J, Davis J (1995) Nature 378:492–496; Das A, Gilbert CD (1999) Nature 399:655–661; Jones HE, Wang W, Sillito AM (2002) J Neurophysiol 88:2797–2808]. In this article, we construct a computational model in programming environment TiViPE [Lourens T (2004) TiViPE—Tino’s visual programming environment. In: The 28th Annual International Computer Software & Applications Conference, IEEE COMPSAC 2004, pp 10–15] of orientation contrast type of cells and demonstrate that the model closely resembles the functional behavior of the neuronal responses of non-orientation (within the CRF) sensitive 4Cβ cells [Jones HE, Wang W, Sillito AM (2002) J Neurophysiol 88:2797–2808], and give an explanation of the indirect information flow in V1 that explains the behavior of orientation contrast sensitivity. The computational model of orientation contrast cells demonstrates excitatory responses at edges near junctions that might facilitate junction detection, but the model does not reveal perceptual pop-out.     

On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409–422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al. (SIAM Journal on Control and Optimization 31(2):387–438, 1993) and Luckhaus and Sturzenhecker (Calculus of Variations and Partial Differential Equations 3(2):253–271, 1995), and show how the corresponding problems can be solved with sub-pixel accuracy using Parametric Maximum Flow techniques. This provides interesting algorithms for computing crystalline curvature motion, possibly with a forcing term. A. Chambolle’s research supported by ANR project “MICA”, grant ANR-08-BLAN-0082. J. Darbon’s research supported by ONR grant N000140710810.     

On Covering Problems of Rado

T. Rado conjectured in 1928 that if ℱ is a finite set of axis-parallel squares in the plane, then there exists an independent subset ℐ⊆ℱ of pairwise disjoint squares, such that ℐ covers at least 1/4 of the area covered by ℱ. He also showed that the greedy algorithm (repeatedly choose the largest square disjoint from those previously selected) finds an independent set of area at least 1/9 of the area covered by ℱ. The analogous question for other shapes and many similar problems have been considered by R. Rado in his three papers (in Proc. Lond. Math. Soc. 51:232–264, 1949; 53:243–267, 1951; and J. Lond. Math. Soc. 42:127–130, 1968) on this subject. After 45 years, Ajtai (in Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 21:61–63, 1973) came up with a surprising example disproving T. Rado’s conjecture. We revisit Rado’s problem and present improved upper and lower bounds for squares, disks, convex bodies, centrally symmetric convex bodies, and others, as well as algorithmic solutions to these variants of the problem.     

The effects of scent and game play experience on memory of a virtual environment

Scent has been well documented as having significant effects on emotion (Alaoui-Ismaili in Physiol Behav 62(4):713–720, 1997; Herz et al. in Motiv Emot 28(4):363–383, 2004), learning (Smith et al. in Percept Mot Skills 74(2):339–343, 1992; Morgan in Percept Mot Skills 83(3)(2):1227–1234, 1996), memory (Herz in Am J Psychol 110(4):489–505, 1997) and task performance (Barker et al. in Percept Mot Skills 97(3)(1):1007–1010, 2003). This paper describes an experiment in which environmentally appropriate scent was presented as an additional sensory modality consistent with other aspects of a virtual environment called DarkCon. Subjects’ game play habits were recorded as an additional factor for analysis. Subjects were randomly assigned to receive scent during the VE, and/or afterward during a task of recall of the environment. It was hypothesized that scent presentation during the VE would significantly improve recall, and that subjects who were presented with scent during the recall task, in addition to experiencing the scented VE, would perform the best on the recall task. Skin-conductance was a significant predictor of recall, over and above experimental groups. Finally, it was hypothesized that subjects’ game play habits would affect both their behavior in and recall of the environment. Results are encouraging to the use of scent in virtual environments, and directions for future research are discussed. The project described herein has been sponsored by the US Army Research, Development, and Engineering Command (RDECOM). Statements and opinions expressed do not necessarily reflect the position or the policy of the US Government; no official endorsement should be inferred.     

On the Behavior of True and False

Uzquiano (Analysis 70:39–44, 2010) showed that the Hardest Logic Puzzle Ever (HLPE) [in its amended form due to Rabern and Rabern (Analysis 68:105–112, 2008)] has a solution in only two questions. Uzquiano concludes his paper by noting that his solution strategy naturally suggests a harder variation of the puzzle which, as he remarks, he does not know how to solve in two questions. Wheeler and Barahona (J Philos Logic, to appear, 2011) formulated a three question solution to Uzquiano’s puzzle and gave an information theoretic argument to establish that a two question solution for Uzquiano’s puzzle does not exist. However, their argument crucially relies on a certain conception of what it means to answer self-referential yes–no questions truly and falsely. We propose an alternative such conception which, as we show, allows one to solve Uzquiano’s puzzle in two questions. The solution strategy adopted suggests an even harder variation of Uzquiano’s puzzle which, as we will show, can also be solved in two questions. Just as all previous solutions to versions of HLPE, our solution is presented informally. The second part of the paper investigates the prospects of formally representing solutions to HLPE by exploiting theories of truth.     

On the air damping of flexible microbeam in free space at the free-molecule regime

Predicting air damping is crucial in the design of high Q microelectromechanical systems. In the past, air damping of rigid microbeam in free space at molecular regime is usually estimated using the free molecular model proposed by Christian (Vacuum 16:175–178, 1966), air damping of flexible microbeam is estimated using the model proposed by Blom (J Vac Sci Technol B 10:19–26, 1992). The relation between the two models is Q _Blom = 3Q _Christian. In this paper, a general proof is presented that shows the Christian’s model is valid for the air damping of flexible microbeam in free space at molecular regime. By comparing with the experimental results available in the literatures (Blom et al. in J Vac Sci Technol B 10:19–26, 1992; Yasumura et al. in J Micromech Syst 9:117–125, 2000), we conclude that the Christian’s model is the best choice in predicting the air damping of flexible microbeam in free space at the molecular regime.     

Approximation Algorithms for Reconstructing the Duplication History of Tandem Repeats

Computing the duplication history of a tandem repeated region is an important problem in computational biology (Fitch in Genetics 86:623–644, 1977; Jaitly et al. in J. Comput. Syst. Sci. 65:494–507, 2002; Tang et al. in J. Comput. Biol. 9:429–446, 2002). In this paper, we design a polynomial-time approximation scheme (PTAS) for the case where the size of the duplication block is 1. Our PTAS is faster than the previously best PTAS in Jaitly et al. (J. Comput. Syst. Sci. 65:494–507, 2002). For example, to achieve a ratio of 1.5, our PTAS takes O(n ⁵) time while the PTAS in Jaitly et al. (J. Comput. Syst. Sci. 65:494–507, 2002) takes O(n ¹¹) time. We also design a ratio-6 polynomial-time approximation algorithm for the case where the size of each duplication block is at most 2. This is the first polynomial-time approximation algorithm with a guaranteed ratio for this case. Part of work was done during a Z.-Z. Chen visit at City University of Hong Kong.     

On body shapes providing maximum depth of penetration

The problem of maximization of the depth of penetration of rigid impactor into semi-infinite solid media (concrete shield) is investigated analytically and numerically using two-stage model and experimental data of Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997). The shape of the axisymmetric rigid impactor has been taken as an unknown design variable. To solve the formulated optimization problem for nonadditive functional, we expressed the depth of penetration (DOP) under some isoperimetric constraints. We apply approaches based on analytical and qualitative variational methods and numerical optimization algorithm of global search. Basic attention for considered optimization problem was given to constraints on the mass of penetrated bodies, expressed by the volume in the case of penetrated solid body and by the surface area in the case of penetrated thin-walled rigid shell. As a result of performed investigation, based on two-term and three-term two stage models proposed by Forrestal et al. (Int J Impact Eng 15(4):396–405, 1994), Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997) and effectively developed by Ben-Dor et al. (Comp Struct 56:243–248, 2002, Comput Struct 81(1):9–14, 2003a, Int J Solids Struct 40(17):4487–4500, 2003b, Mech Des Struct Mach 34(2): 139–156, 2006), we found analytical and numerical solutions and analyzed singularities of optimal forms.     

Thwarting intercept-and-resend attack on Zhang’s quantum secret sharing using collective rotation noises

This work deliberately introduces collective-rotation noise into quantum states to prevent an intercept-resend attack on Zhang’s quantum secret sharing scheme over a collective-noise quantum channel (Zhang in Phys A 361:233–238, 2006). The noise recovering capability of the scheme remains intact. With this design, the quantum bit efficiency of the protocol is doubled when compared to Sun et al.’s improvement on Zhang’s scheme (Sun et al. in Opt Commun 283:181–183, 2010).     

Effects of planar inlet plenums on the hydrodynamically developing flows in rectangular microchannels of complementary aspect ratios

The effects of planar inlet plenum geometry on the developing flow fields in two rectangular microchannels of reciprocal aspect ratios (H/W ∼2.75 and ∼0.40) were investigated for Re _D =  1–100 using micro particle image velocimetry (μPIV). These two microchannels were made by a precision sawing and silicon microfabrication techniques. Both the velocity profiles and centerline velocity developments were clearly resolved and extracted along the axial distance from μPIV results. The entrance lengths were found from the centerline velocities using a decaying exponential fitting function where the centerline velocity reaches 99% of the fully developed centerline velocity. The proposed fitting function showed excellent agreement with the experimental results. The planar plenum was shown to cause an upstream predevelopment resulting in the significant reductions in the entrance lengths. Two entrance length correlations were proposed in the forms of Atkinson et al.’s (AIChE J 15:548–553, 1969) and Chen’s (J Fluids Eng 95:153–158, 1973) correlations. The proposed entrance length correlations showed that acquired constant portion and slope of the entrance lengths showed 23–27 and 70–81% reductions for H/W =  2.75 while the entrance length correlation for H/W =  0.40 showed 69–73% increase and 41–63% decrease in the constant portion and slope, respectively.     

Models of Greedy Algorithms for Graph Problems

Borodin et al. (Algorithmica 37(4):295–326, 2003) gave a model of greedy-like algorithms for scheduling problems and Angelopoulos and Borodin (Algorithmica 40(4):271–291, 2004) extended their work to facility location and set cover problems. We generalize their model to include other optimization problems, and apply the generalized framework to graph problems. Our goal is to define an abstract model that captures the intrinsic power and limitations of greedy algorithms for various graph optimization problems, as Borodin et al. (Algorithmica 37(4):295–326, 2003) did for scheduling. We prove bounds on the approximation ratio achievable by such algorithms for basic graph problems such as shortest path, weighted vertex cover, Steiner tree, and independent set. For example, we show that, for the shortest path problem, no algorithm in the FIXED priority model can achieve any approximation ratio (even one dependent on the graph size), but the well-known Dijkstra’s algorithm is an optimal ADAPTIVE priority algorithm. We also prove that the approximation ratio for weighted vertex cover achievable by ADAPTIVE priority algorithms is exactly 2. Here, a new lower bound matches the known upper bounds (Johnson in J. Comput. Syst. Sci. 9(3):256–278, 1974). We give a number of other lower bounds for priority algorithms, as well as a new approximation algorithm for minimum Steiner tree problem with weights in the interval [1,2]. S. Davis’ research supported by NSF grants CCR-0098197, CCR-0313241, and CCR-0515332. Views expressed are not endorsed by the NSF. R. Impagliazzo’s research supported by NSF grant CCR-0098197, CCR-0313241, and CCR-0515332. Views expressed are not endorsed by the NSF. Some work done while at the Institute for Advanced Study, supported by the State of New Jersey.     

Bidirectional Optimization from Reasoning and Learning in Games

We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998, J Semant 17(3):189–216, 2000) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a process of reinforcement learning with lateral inhibition.     

A New Mapped Weighted Essentially Non-oscillatory Scheme

The weighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Recently Henrick et al. (J. Comput. Phys. 207:542–567, 2005) noted that the fifth-order WENO method by Jiang and Shu (J. Comput. Phys. 126:202–228, 1996) is only third-order accurate near critical points of the smooth regions in general. Using a simple mapping function to the original weights in Jiang and Shu (J. Comput. Phys. 126:202–228, 1996), Henrick et al. developed a mapped WENO method to achieve the optimal order of accuracy near critical points. In this paper we study the mapped WENO scheme and find that, when it is used for solving the problems with discontinuities, the mapping function in Henrick et al. (J. Comput. Phys. 207:542–567, 2005) may amplify the effect from the non-smooth stencils and thus cause a potential loss of accuracy near discontinuities. This effect may be difficult to be observed for the fifth-order WENO method unless a long time simulation is desired. However, if the mapping function is applied to seventh-order WENO methods (Balsara and Shu in J. Comput. Phys. 160:405–452, 2000), the error can increase much faster so that it can be observed with a moderate output time. In this paper a new mapping function is proposed to overcome this potential loss of accuracy.     

On Buckley��s approach to fuzzy estimation

In several works, Buckley (Soft Comput 9:512–518, 2005a; Soft Comput 9:769–775 2005b; Fuzzy statistics, Springer, Heidelberg, 2005c) have introduced and developed an approach to the estimation of unknown parameters in statistical models. In this paper, we introduce an improved method for the estimation of parameters for cases in which the Buckley’s approach presents some drawbacks, as for example when the underlying statistic has a non-symmetric distribution.     

A note on the alternating group network

The class of alternating group networks was introduced in the late 1990’s as an alternative to the alternating group graphs as interconnection networks. Recently, additional properties for the alternating group networks have been published. In particular, Zhou et al., J. Supercomput (2009), doi:, was published very recently in this journal. We show that this so-called new interconnection topology is in fact isomorphic to the (n,n−2)-star, a member of the well-known (n,k)-stars, 1≤k≤n−1, a class of popular networks proposed earlier for which a large amount of work have already been done. Specifically, the problem in Zhou et al., J. Supercomput (2009), doi:, was addressed in Lin and Duh, Inf. Sci. 178(3), 788–801, 2008, when k = n−2.     

All-Pairs Shortest Paths with Real Weights in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>3</Superscript>/log <Emphasis Type="Italic">n</Emphasis>) Time

We describe an O(n ³/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones. A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.