A New Approach for Firm Value and Default Probability Estimation beyond Merton Models

In this paper we present a new model to assess the firm value and the default probability by using a bivariate contingent claim analysis and copula theory. First we discuss an unfeasible case, given the current derivative market on corporate bonds, which involves univariate digital options to compute the risk neutral probabilities. We then discuss a feasible model, which considers risky interest rates, instead. Moreover, we develop in this framework a new methodology to extract default probabilities from stock prices, only, going beyond the standard KMV-Merton model. Besides, the non-observability of the Merton model’s state variable requires numerical methods, but the results can be unstable with noisy risky data. We show how the null price can be used as a useful barrier to separate an operative firm from a defaulted one, and to estimate its default probability. We then present an empirical application with both operative and defaulted firms to show the advantages of our approach.      

Factorization of fuzzy concept lattices with hedges by modification of input data

We study the problem of reducing the size of fuzzy concept lattices with hedges by means of factorization. As it has been shown previously for the case of fuzzy concept lattices without hedges, the lattice computed by factorization of a fuzzy concept lattice is isomorphic to a fuzzy concept lattice of some other data table. This means that the factor concept lattice can be computed directly as a concept lattice, whose underlying data table is obtained by a modification of the original data table. There are two known types of such a modification: first, based on factorization of residuated lattices, and second, based on computation of shifted attributes. In this paper, we extend these results to a more general case of concept lattices with hedges.     

Rotational sandpile models: A finite size scaling study

Nontrivial critical behaviour is observed in equilibrium lattice statistical models under rotational constraint. Effect of rotational constraint on lattice statistical models at out of equilibrium situation is important to study. Critical properties of non-equilibrium steady state of sandpile models are studied under rotational constraint via finite size scaling (FSS) analysis. Not only FSS is found to be valid for a wide range of rotational sandpile models but also they are found to belong to the same universality class.     

Finding consensus in speech recognition: word error minimization and other applications of confusion networks

We describe a new framework for distilling information from word lattices to improve the accuracy of the speech recognition output and obtain a more perspicuous representation of a set of alternative hypotheses. In the standard MAP decoding approach the recognizer outputs the string of words corresponding to the path with the highest posterior probability given the acoustics and a language model. However, even given optimal models, the MAP decoder does not necessarily minimize the commonly used performance metric, word error rate (WER). We describe a method for explicitly minimizing WER by extracting word hypotheses with the highest posterior probabilities from word lattices. We change the standard problem formulation by replacing global search over a large set of sentence hypotheses with local search over a small set of word candidates. In addition to improving the accuracy of the recognizer, our method produces a new representation of a set of candidate hypotheses that specifies the sequence of word-level confusions in a compact lattice format. We study the properties of confusion networks and examine their use for other tasks, such as lattice compression, word spotting, confidence annotation, and reevaluation of recognition hypotheses using higher-level knowledge sources.     

Feedback,causality and distance between arma models

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR representation is greater than a certain number that is a function of p, then Granger causality must exist in at least one direction in the variables.     

3D crystal structure identification using fuzzy neural networks

The problem of recognizing nano-scale images of lattice projections comes down to identification of crystal lattice structure. The paper considers two types of fuzzy neural networks that can be used for tackling the problem at hand: the Takagi-Sugeno-Kang model and Mamdani-Zadeh model (the latter being a modification of the Wang-Mendel fuzzy neural network). We offer a threestage neural network learning process. In the first two stages crystal lattices are grouped in non-overlapping classes, and lattices belonging to overlapping classes are recognized at the third stage. In the research, we thoroughly investigate the applicability of the neural net models to structure identification of 3D crystal lattices.     

Hybrid analysis of SGSPNs with time-dependent transition rates

For the class superposed generalized stochastic Petri nets (SGSPNs), we present a new analysis algorithm which combines the ideas of transient numerical analysis via uniformization and discrete event simulation. Simulation is used to determine the firing times of synchronized transitions describing interactions between the components of an SGSPN. Numerical analysis is used to compute the distribution of states between firing times of synchronized transitions. The approach avoids handling vectors of the size of the state space and can therefore be used for models with a huge state space which cannot be analyzed with numerical analysis techniques. On the other hand, the approach allows the computation of reliable estimates for results based on small probabilities or rare events which cannot be analyzed with simulation. As a byproduct of the handling of synchronized transitions using simulation, it is possible to extend the class of SGSPNs by allowing synchronized transitions with time-dependent transition rates.     

Polynomial Algorithms for Pricing Path-Dependent Interest Rate Instruments

In this paper we study algorithms for pricing of interest rate instruments using recombining tree (scenario lattice) interest models. The price is defined as expected discounted cash flow. If the cash-flow generated by the instrument depends on the full or partial history of interest rates (path-dependent contracts), then pricing algorithms are typically of exponential complexity. We show that for some models, including product form cash-flows, additive cash-flows, delayed cash-flows and limited path-dependent cash-flows, polynomial pricing algorithms exist.     

Retailoring Box Splines to Lattices for Highly Isotropic Volume Representations

3D box splines are defined by convolving a 1D box function with itself along different directions. In volume visualization, box splines are mainly used as reconstruction kernels that are easy to adapt to various sampling lattices, such as the Cartesian Cubic (CC), Body‐Centered Cubic (BCC), and Face‐Centered Cubic (FCC) lattices. The usual way of tailoring a box spline to a specific lattice is to span the box spline by exactly those principal directions that span the lattice itself. However, in this case, the preferred directions of the box spline and the lattice are the same, amplifying the anisotropic effects of each other. This leads to an anisotropic volume representation with strongly preferred directions. Therefore, in this paper, we retailor box splines to lattices such that the sets of vectors that span the box spline and the lattice are disjoint sets. As the preferred directions of the box spline and the lattice compensate each other, a more isotropic volume representation can be achieved. We demonstrate this by comparing different combinations of box splines and lattices concerning their anisotropic behavior in tomographic reconstruction and volume visualization.     

Solving the parity problem in one-dimensional cellular automata

The parity problem is a well-known benchmark task in various areas of computer science. Here we consider its version for one-dimensional, binary cellular automata, with periodic boundary conditions: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. Since the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1), it suffices to account for odd-sized lattices only. We are interested in determining the minimal neighbourhood size that allows the problem to be solvable for any arbitrary initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can solve the parity problem, even in the simpler case of prime-sized lattices. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem; however, we review recent data against a solution in radius 3, thus providing strong empirical evidence that there may not exist a radius 3 solution even for prime-sized lattices only, contrary to a recent conjecture in the literature.     

A basic lattice model of an excitable medium: Kinetic Monte Carlo simulations

The simplest stochastic lattice model of an excitable medium is considered. Each lattice cell can be in one of three states: excited, refractory, or quiescent. Transitions between different cell states occur with the prescribed probabilities. The model is designed for studying the transfer of excitation in the cardiac muscle and nerve fiber at the cellular and subcellular levels, and also for modeling the spreading of epidemics. Elementary events on the lattice are simulated by the kinetic Monte Carlo method, which consists in constructing a Markov chain of the lattice states corresponding to the solution of the master equation. An effective algorithm for implementing the Kinetic Monte Carlo simulations is suggested. The number of the arithmetic operations at each time step of the proposed algorithm is practically independent of the lattice size, which enables making calculations on two- and three-dimensional lattices of a very large size (more than 10⁹ cells). It is shown that the model reproduces the basic spatiotemporal structures (solitary traveling pulses, pulse trains, concentric and spiral waves, and spiral turbulence) characteristic of an excitable medium. The basic properties of traveling pulses and spiral waves for the considered stochastic lattice model are studied and compared with the known properties of deterministic equations of the reaction-diffusion type, which are usually employed for modeling excitable media.     

位置相关信息服务中的一种数据预取方法

位置相关信息服务中访问数据涉及到复杂的空间计算,导致访问数据的延迟时间较长,而数据预取能够显著提高数据的访问速度,缩短访问数据的时间。基于LDD的预取策略如DDP考虑了数据距离,但是没有考虑数据的访问概率和更新频率及数据大小。针对以上问题提出基于价值的数据预取（CDP）策略,一些重要的数据预取因素如访问概率、更新频率、数据项大小、数据距离和有效范围等都包含在价值函数里,根据价值函数值的大小来选择被预取的数据。通过实验对比,CDP比DDP策略能更有效的提高缓存命中率。     

李群机器学习(LML)的学习子空间轨道生成格算法

给出了李群机器学习（LML）的学习子空间轨道生成格及相关的基本概念,包括：李群机器学习中的样例数据集,轨道生成格理论及其算法,同时也给出了实例验证分析,并与决策树学习算法C4.5作比较,在分类的正确性方面优于C4.5算法,由此进一步证明了该理论的可行性以及算法的有效性。     

LATTICES OF STRUCTURE MODELS AND DATABASE SCHEMES

This paper deals with basic properties of lattices of structure models. The form of models considered here is used in at least three areas: reconstructabilily analysis, analysis of contingency tables, and relational and probabilistic database design. The fact that the set of all models is structured as a lattice has been part of the basic formulation of problems in reconstructabilily analysis, while in the other two areas this aspect, while not necessarily less important, has represented o less major line of development

Various class of the models are considered here. The paper characterizes and explores lattice properties of these classes of models, and develops means to make structural comparisons among them, including definition of a structural distance with which the lattice of models is a metric lattice. The paper includes a proof of the modularity of the lattices and of a formula for determining their height, as well as a number of algorithms for determining the structural distance

The paper gives a detailed consideralion of a strategy for partition search of the lattice of models and defines a recursive Boolean lattice as a data structure that extends the partition search strategy by recursive partioning.     

Continuous models for 2D discrete media valid for higher-frequency domain

The paper is focused on 2D continuous models derived from a discrete micro-structure. A new continualization procedure that refers to the non-local interaction between variables of the discrete media is proposed. The proposed procedure covers mainly the application of two-point Padé approximations and allows us to obtain continuous models suitable for analysis of 2D lattice vibrations with arbitrary frequencies.     

DIRECTED SYSTEMS LATTICES IN RECONSTRUCTABILITY ESTIMATION

Abstract

The progression from neutral systems to directed systems is natural given the identification of generating variables in the mask analysis process of the General Systems Problem Solver. Any overall system of n variables may be represented by n-1 lattices of structures, each lattice containing 1 ≤ α < n input variables and β = n - α generated variables. The structures comprising each lattice are composed of a combination of environmental input generating-input, generating-output, neutral, and generated variables. Structures which contain one or more neutral variables ate called semi-directed or s-structures, and structures which do not contain neutral variables are called fully-directed or d-structures. Any s-structure can be evaluated into two or more d-structures. Catalogues of s-structure lattices for n = 3 and 4 variables are given     

Single- and Multiobjective Optimization on the Lattice of Cubes

This paper gives examples of optimization problems on a lattice of cubes in the single- and multiobjective cases. We describe a method for calculating the local curvature of a given surface of a large-area geological object at each point and for constructing its curvature surface based on these geophysical data. Such information is used in geology and geophysics for detecting the most probable storage areas of hydrocarbons [1–5]. Based on these results, we develop mathematical models and state single- and multiobjective optimization problems on a lattice of cubes for arranging a finite number of oil wells in an explored field. We describe a method for designing an equivalence set for solving multiobjective problems on the lattices of cubes of any dimensions. Finally, we show that a similar approach is applicable for stating and solving optimization problems on a lattice of cubes in different sectors of the economy.     

同义概念格的纵向合并

由于概念格自身的完备性,构造效率一直是制约其进一步应用的瓶颈。本文从概念格的构造入手,提出了同义概念格的观点,并利用其性质进一步提出了一种纵向合并同义概念格的算（VUSCL算法）。实验表明,随着节点数的增加,该算法与文献[8]中的纵向合并算法相比,其时间性能有明显改善。     

Efficient Venn predictors using random forests

Successful use of probabilistic classification requires well-calibrated probability estimates, i.e., the predicted class probabilities must correspond to the true probabilities. In addition, a probabilistic classifier must, of course, also be as accurate as possible. In this paper, Venn predictors, and its special case Venn-Abers predictors, are evaluated for probabilistic classification, using random forests as the underlying models. Venn predictors output multiple probabilities for each label, i.e., the predicted label is associated with a probability interval. Since all Venn predictors are valid in the long run, the size of the probability intervals is very important, with tighter intervals being more informative. The standard solution when calibrating a classifier is to employ an additional step, transforming the outputs from a classifier into probability estimates, using a labeled data set not employed for training of the models. For random forests, and other bagged ensembles, it is, however, possible to use the out-of-bag instances for calibration, making all training data available for both model learning and calibration. This procedure has previously been successfully applied to conformal prediction, but was here evaluated for the first time for Venn predictors. The empirical investigation, using 22 publicly available data sets, showed that all four versions of the Venn predictors were better calibrated than both the raw estimates from the random forest, and the standard techniques Platt scaling and isotonic regression. Regarding both informativeness and accuracy, the standard Venn predictor calibrated on out-of-bag instances was the best setup evaluated. Most importantly, calibrating on out-of-bag instances, instead of using a separate calibration set, resulted in tighter intervals and more accurate models on every data set, for both the Venn predictors and the Venn-Abers predictors.