Some stochastic Leontief-Ford models and their deterministic equivalents

Some stochastic Leontief-Ford models of ecological-economic interaction and their deterministic equivalents are proposed. A theory of stochastic variants of ecological-economic structural-type functions is developed. Appropriate algorithms are developed. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–10, May–June 2007.     

Remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances

A persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in [1]. In this note we give a direct and simple proof for the case of bounded signals of the result of [1] and show, via a counterexample, that an assumption on system signals boundedness which does not appear in [1] is necessary when arbitrary unbounded signals are allowable. Finally, we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component.     

Remarks on stochastic model reduction

In this note, we give a solution to the stochastic system model reduction problem in terms of the approximation of the output stochaslic process power spectrum by applying balanced realization or optimal Hankel norm approximation to the asymptotically stable and minimum phase spectral factor. We also give explicit bounds for the approximation error. The effectiveness of this method is compared to the one by Jonckheere and Helton.     

The calibration of stochastic local-volatility models: An inverse problem perspective

We tackle the calibration of the Stochastic Local-Volatility (SLV) model. This is the class of financial models that combines the local volatility and stochastic volatility features and has been subject of the attention by many researchers and practitioners recently. The corresponding inverse problem consists in finding certain (functional) coefficients in a class of parabolic partial differential equations from observed values of the solutions. More precisely, given a calibrated local volatility surface and a choice of stochastic volatility parameters, we calibrate the corresponding leverage function. Our approach makes use of regularization techniques from inverse-problem theory, respecting the integrity of the data and thus avoiding data interpolation. The result is a stable and efficient algorithm which is resilient to instabilities in the regions of low probability density of the spot price and of the instantaneous variance. We substantiate our claims with numerical experiments using synthetic and real data.     

Remarks on the makespan minimization problem

In this brief article we consider the worst-case performance of a heuristic proposed for the problem of minimizing the overall completion time in scheduling a collection of independent tasks to a system of identical processors. It has been suggested that this heuristic, based on the familiar LPTrule, possesses a vastly improved worst-case behavior. We demonstrate that it instead shares LPT's asymptotic worst-case performance bound of 4/3.     

CURIE: a cellular automaton for concept drift detection

Data Mining and Knowledge Discovery - Data stream mining extracts information from large quantities of data flowing fast and continuously (data streams). They are usually affected by changes in the...     

Creating non-minimal triangulations for use in inference in mixed stochastic/deterministic graphical models

We demonstrate that certain large-clique graph triangulations can be useful for reducing computational requirements when making queries on mixed stochastic/deterministic graphical models. This is counter to the conventional wisdom that triangulations that minimize clique size are always most desirable for use in computing queries on graphical models. Many of these large-clique triangulations are non-minimal and are thus unattainable via the popular elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs needs to be considered when searching for state space optimal triangulations in such graphs. Empirical results on random and real world graphs are given. We also present an algorithm and correctness proof for determining if a triangulation can be obtained via elimination, and we show that the decision problem associated with finding optimal state space triangulations in this mixed setting is NP-complete.     

Multiterminal global routing: A deterministic approximation scheme

We consider the problem of routing multiterminal nets in a two-dimensional gate-array. Given a gate-array and a set of nets to be routed, we wish to find a routing that uses as little channel space as possible. We present a deterministic approximation algorithm that uses close to the minimum possible channel space. We cast the routing problem as a new form of zero-one multicommodity flow, an integer-programming problem. We solve this integer program approximately by first solving its linear-program relaxation and then rounding any fractions that appear in the solution to the linear program. The running time of the rounding algorithm is exponential in the number of terminals in a net but polynomial in the number of nets and the size of the array. The algorithm is thus best suited to cases where the number of terminals on each net is small.     

Multiterminal global routing: A deterministic approximation scheme

We consider the problem of routing multiterminal nets in a two-dimensional gate-array. Given a gate-array and a set of nets to be routed, we wish to find a routing that uses as little channel space as possible. We present a deterministic approximation algorithm that uses close to the minimum possible channel space. We cast the routing problem as a new form of zero-one multicommodity flow, an integer-programming problem. We solve this integer program approximately by first solving its linear-program relaxation and then rounding any fractions that appear in the solution to the linear program. The running time of the rounding algorithm is exponential in the number of terminals in a net but polynomial in the number of nets and the size of the array. The algorithm is thus best suited to cases where the number of terminals on each net is small.This work was done while the authors were with the Computer Science Division, University of California at Berkeley. The work of Prabhakar Raghavan was supported by an IBM Doctoral Fellowship, and the work of Clark Thompson was supported by a California State MICRO grant (AT&T Foundation).     

A universal cellular automaton in the hyperbolic plane

The paper gives the construction of a universal CA with 22 states in the regular rectangular pentagonal grid of the hyperbolic plane. The CA implements a railway circuit which simulates a register machine and which improves a bit already known railway simulations of a Turing machine.     

An application of the stochastic automaton to the investment game

An application of the stochastic automaton to the investment game is considered. It is shown that the use of the stochastic automaton with learning properties is an efficient method for the investment game.     

A simplified combat model based on a cellular automaton

The work is devoted to constructing a cellular automaton based model of motion and combat activity of systems of hierarchically organized agents with allowance for terrain ruggedness, communication channels between the agents, and the necessity of choosing behavior adequate to the current situation.     

A global algorithm for minimax solutions to a stochastic programming problem

A minimax solution to a stochastic program occurs when the objective function is maximized subject to the random parameters jointly taking on their most adverse or pessimistic values. Minimax solutions have been proposed for decision making in agricultural planning, and to provide a lower bound to the values of the objective function of the “wait and see” stochastic program. In this paper a non-convex minimax problem and the occurrence of local optima are discussed. A global algorithm is presented for the minimax problem of a stochastic program in which some of the right hand side parameters are stochastic. It is also shown how minimax solutions may be obtained where stochastic parameters occur solely in the objective function, and in the objective function and right hand sides simultaneously.     

A weakly universal cellular automaton on the pentagrid with two states

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with two states. This paper improves in some sense a previous result with three states. Both results make use of a la Moore neighbourhood. However, the result with three states is rotation invariant while the result of the present paper is not. In both cases, at each step of the computation, the set of non quiescent states has always infinitely many cycles.     

An efficient hybrid self-learning method for stochastic cellular manufacturing problem: A queuing-based analysis

This paper addresses a new version of Stochastic Mixed-Integer model to design cellular manufacturing systems (CMSs) under random parameters described by continues distributions. In an uncertain environment processing time, part demand, product mix, inter-arrival time and etc. may change over the period of time. Thus, during planning horizon since any of the parameters of the problem may vary widely, design decisions may be in effect. So, in this research to overcome such drawback, it’s assumed that processing time for parts on machines and arrival time for parts to cells are stochastic and described by continues distribution which yields more flexibility to analyze manufacturing framework. In such case, there are some approaches such as stochastic programming (SP), robust optimization (RO) and queuing theory which can formulate and analyze this problem. In this paper, it’s assumed that each machine works as a server and each part is a customer where servers should service to customers. Therefore, formed cells define a queue system which can be optimized by queuing theory. In this way, by optimizing a desired queue system measurement such as maximizing the probability that a server is busy, the optimal cells and part families will be formed. To solve such a stochastic and non-linear model, an efficient hybrid method based on new combination of genetic algorithm (GA) and simulated annealing (SA) algorithm will be proposed where SA is a sub-ordinate part of GA under a self-learning rule (SLR) criterion. This integrative combination algorithm is compared against global solutions obtained from branch-and-bound algorithm and a benchmark heuristic algorithm existing in the literature. Also, sensitivity analysis will be performed to illustrate behavior of the model.     

Alternating time versus deterministic time: A separation

Paulet al. [12] proved that deterministic Turing machines can be speeded up by a factor of log*t (n) using four alternations; that is, DTIME(t(n) log*t(n)) σ₄(t(n)). Balcázaret al. [1] noted that two alternations are sufficient to achieve this speed-up of deterministic Turing machines; that is, DTIME(t(n) log*t(n)) Σ₂(t (n)). We supply a proof of this speed-up and using that show that for each time-constructible functiont(n), DTIME(t(n)) ⊂ Σ₂(t(n)); that is, two alternations are strictly more powerful than deterministic time. An important corollary is that at least one (or both) of the immediate generalizations of the result DTIME(n) ⊂ NTIME(n) [12] must be true: NTIME(n) ≠ co-NTIME(n) or, for each time-constructible functiont(n), DTIME(t (n)) ⊂ NTIME(t (n)). This work was supported in part by NSF Grant CCR-8909071. The preliminary version of the work was done when the author was a graduate student at The Ohio State University.     

Planning horizons for the deterministic capacity problem

We consider the problem of determining the optimal timing and sizing of new facility construction under a continuous technology model of possible sizes. The rate of convergence of short to long run optimal policies is established and planning horizon implications are explored. We also present an efficient algorithm for solving such problems for all horizon times by solving a single horizon time problem     

An analysis of the effect of the stochastic component of urban cellular automata models

Urban cellular automata models have proved useful tools in urban growth prediction because of their simplicity and their ability to reproduce complex emergent dynamics. Complex emergent dynamic systems involve processes that are difficult to predict, in which randomness plays a key role. In view of the fact that randomness is particularly relevant to complex processes, the aim of this paper is to analyze the sensitivity of the results of urban cellular automata models to the different methods used to incorporate the stochastic component in the models. The urban growth patterns obtained using different stochastic components are analyzed and compared using a number of spatial metrics. The results show that the differences observed in the simulated patterns are sufficiently relevant to justify the need for this type of analysis, which allows for the selection of the stochastic component that best suits the dynamics of the area.     

Halting the hallmarks: a cellular automaton model of early cancer growth inhibition

Cancer treatment is a fragmented and varied process, as “cancer” is really hundreds of different diseases. The “hallmarks of cancer” proposed by Hanahan and Weinberg (Cell 100(1):57–70, 2000) are a framework for viewing cancer within a common set of underlying principles—ten properties that are common to almost all cancers, allowing them to grow uncontrollably and ravage the body. We used a cellular automaton model of tumour growth paired with lattice Boltzmann methods modelling oxygen flow to simulate combination drugs targeted at knocking out pairs of hallmarks. We found that knocking out some pairs of cancer-enabling hallmarks did not prevent tumour formation, while other pairs significantly prevent tumour growth (\(p=0.0004\) using Wilcoxon signed-rank adjusted with the Bonferroni correction for multiple comparisons). This is not what would be expected from models of knocking out the hallmarks individually, as many pairs did not have an additive effect but had either no statistically significant effect or a multiplicative one. We propose that targeting certain pairs of cancer hallmarks, specifically cancers ability to induce blood vessel development paired with another cancer hallmark, could prove an effective cancer treatment option.