... \let
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...\space [*]
The favorable exceptions are the Markovian processes including the Wiener one. Extending the Wiener process to $m >1$ the Markovian property disappears. 
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... randomization[*]
The randomization means that a decision depends on some random variable included into an algorithm deliberately. 
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...#tex2html_wrap_inline379#[*]
Meaning that a randomization is applied. For example:
- generate an uniformly distributed random number $\xi \in [0,1]$
- take a decision $j$ if $\xi < r_j$, where $\rho_x(h_j)$ is an increasing function of $h_j$ and $x=(x_1,...,x_m)$ is a parameter vector. 
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... possible[*]
In this case the solution time is inversely proportional to the number of parallel processors. 
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... outperform[*]
In terms of average errors. 
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... problems[*]
No polynomial time algorithm has been found for solving the NP-complete problems. No proof is known that these problems cannot be solved in polynomial time. 
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... probability[*]
That can be understood as a lottery with the probability $r(m)$ to win a collection $m$. This lottery can be carried out by generating a random number $\xi$ uniformly distributed in $[0,1]$ and by selecting a collection $m$ if $\xi < r(m)$. 
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... feasible[*]
Satisfying inequality (2.2). 
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... list[*]
Initially the starting list includes all the objects 
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...#tex2html_wrap_inline1032#[*]
The algorithm is implemented in C++ and Java in the files $fi.C$ and $Knapsack.java$ correspondingly (see section 4 for details). 
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... feasible[*]
Assume for simplicity that all the non feasible collections are eliminated automatically. 
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...#tex2html_wrap_inline1208#[*]
If by chance the same mutant $m=m^+=m^-$ will be selected then repeat the selection procedure. 
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... value[*]
The sign is minus, because by default GMJ reduces the objective of the Task object. 
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... cost[*]
Including the direct cost and indirect benefits and losses. 
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... reactors[*]
Assuming that the sequence of reactors is not uniquely determined by the technological processes. 
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... new[*]
New means that the city is not visited yet. 
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... "expensive"[*]
In a sense of computing time. 
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... REQP[*]
In later versions a different algorithm [Schittkowski, 1985] is implemented under the name NLP. 
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... formulae[*]
in LBAYES those formulae are included in the algorithm, therefore no additional reduction is needed. 
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...#tex2html_wrap_inline2751#[*]
This is the well known Rastrigin test function [Rastrigin, 1968]. 
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... BACKSPACE[*]
One should use the 'xmodmap' command to adapt the keymap, if the BACKSPACE key is not working. 
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... objects[*]
These objects are implemented in the JDK1.2 version (GMJ2). 
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... JDK1.0.x[*]
The command 'appletviewer' may not work properly, if one uses JDK1.1 or higher. That is a disadvantage of GMJ0. 
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... 'upperBounds'[*]
zero element defines the first element and so on. 
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... correspondingly[*]
Note that the constructor of class Task can be deleted if one is satisfied by the default values. 
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... appletviewers[*]
For example, by the command
$appletviewer\ http://optimum.mii.lt/~jonas/gmj2j/gmj.html$. 
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... times[*]
These compilers are available in JDK1.1, too, starting from JDK1.1.7. 
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... window[*]
This window can be open by selecting the $Spectrum$ mode on the $Convergence$ menu. 
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... frequency[*]
Defined by different colors. 
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... Mead[*]
This is a reduced Flexi version. Only rectangular constraints are implemented. 
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... variables[*]
Note, that in GMJ2 the feasible set is given by a user defined $constraint$ function. Therefore, there are no restrictions on the shape of feasible set. 
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... files[*]
In the "applet.html" file one can list several $jar$ files. 
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... constraints[*]
By "non-rectangular" we mean constraints defined as a system of linear and nonlinear equations and inequalities. 
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... value[*]
The default value is 1. 
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... multipliers[*]
Defined by minimizing the Lagrange function corresponding to each server. 
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... cost[*]
It is. assumed for simplicity that the waiting cost is equal to an average waiting time. 
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... equilibrium[*]
If the equilibrium exists. 
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... [*]
That explains the acronym NLA(p). 
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...#tex2html_wrap_inline6323#[*]
As defined by expressions (11.4) and (11.6). 
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... equilibrium[*]
If the equilibrium exists. 
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... equilibrium[*]
If the equilibrium exists. 
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...#tex2html_wrap_inline6477#[*]
As defined by expressions (11.4) and (11.6). 
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... equilibrium[*]
If the equilibrium exists. 
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... server[*]
For simplicity, it is assumed that "time-is-money" and that a unit of time cost a unit of money, in the real life cases the corresponding coefficients should be included 
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...#tex2html_wrap_inline7751#[*]
The variables $x,y$ obtain different meanings, if one uses mixed strategies. That reduces the number of symbols. To avoid confusion, the utilities $U_a(x,y),V_a(x,y)$ are supplied with the subscript $a$. If the subscript $a$ is absent then $x,y$ defines the parameters $z_0,w_0,a,b,t_1,t_2$. Otherwise, $x,y$ denotes mixed strategies. 
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...custd)[*]
This means that the customer balance follows the changes of parameters $y_i(t)$ and $x_i(t)$ almost without delay. 
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... violation[*]
For example, killing prey. 
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... detected[*]
The prey is killed and a poacher is caught. 
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... violation[*]
The value of the killed prey. 
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... violation[*]
For example, stealing goods. 
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... detected[*]
Goods are not stolen and the thief is caught. 
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... games[*]
In the inspector game, there is no equilibrium in pure strategies if $g_i=g$ and $q_i=q$, see (13.68). 
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... irrelevant[*]
The fraud is irrelevant, if average winnings of the partner does not depend on his pure strategy $i=1,...,m$, and vice versa 
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... calculations[*]
One can see that the calculations do not correspond exactly to the QSE algorithm because this is an experimental software. The updated software is under development. 
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... objects[*]
The optimal decision $x=1/m$ is not unique, any decision satisfying the inequality $c_i x_i \ge a,\ i=1,...,m$ minimizes the expected utility function $U(y)$. 
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... investments[*]
The actual investment is the product of the total investment and the relative investment, divided by the sum of all the relative investments. 
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... number[*]
Different frequencies are is denoted by different colors. 
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... confident[*]
Without the "confidence" assumption one should consider stock rates predictions errors, too. 
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... files[*]
The data file is on the web-sites (see Section 4). 
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... normalization[*]
Users make the normalization in this software version. 
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... securities[*]
CD and Stocks. 
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... cases[*]
By the term `difficult' we mean the time measure of computational complexity, that is, the length of time would be needed for a standard universal computer to do a task. 
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...#tex2html_wrap_inline11397#[*]
The notation $P=NP$ means the existence a polynomial-time algorithm $P$ for solving $NP$-complete problems. That is merely a theoretical possibility. 
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... known[*]
For example, while predicting call rates we know in advance such "external" factors as holidays, vacation times, e.t.c. 
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...#tex2html_wrap_inline11677#[*]
This is true, if the activation function $\phi$ is non-linear. The linear activation function reduces the ANN model to the standard Auto Regressive (AR)n model. 
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... neuron[*]
The output of the traditional activation function is supposed to be non-negative. 
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... ARFIMA[*]
Often the alternative title ARIMA(p,d,q) is used. 
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...#tex2html_wrap_inline11695#[*]
Note that, contrary to the traditional practice, we do not assume the time series to be stationary. We allow the degree of integration of the series to be detected by direct estimate of the differentiation parameter $d$. 
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... [*]
The same reasoning applies to the log-likelihood function, too. 
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...\space [*]
Note that describing a real data one needs diverse structures including a number of different models, not just one specific model as in this illustrative example. 
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... unstable[*]
The parameters are considered as unstable if they change too much in different data sets. 
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...#tex2html_wrap_inline11957#[*]
The elimination of both continuous parameters $a_1$ and $a_2$ is unfeasible. 
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... bank[*]
A small Lithuanian bank. 
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... ones[*]
Meaning that the sum (15.60) of the ARFIMA model is a non-linear function of the parameters $b$ and $d$. 
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... files[*]
This operation is not permited by browsers, as usuall. 
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... sales[*]
Sales with immediate payment. 
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... sales[*]
Sales with delay of payments. 
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... shares[*]
Shares of company $j$. 
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...#tex2html_wrap_inline12885#[*]
The balance is negative, if the buying expences exceed the selling ones. 
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...#tex2html_wrap_inline14052#[*]
Only two parameters $c$ and $m$ are in $C(c,m)$. The reason is uncertainty of $c$, therefore, the optimization of $m$ is repeated several times at different "scenarios" $c$. 
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... probability[*]
Estimated using the Monte Carlo techniques described in the previous chapter. 
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... server[*]
There are no reserved waiting places for the calls $\lambda_s$, thus the symbols $r_s$ are omitted. 
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... problem[*]
Solution of this problem is difficult, thus, later on we shall consider some simple cases as illustrations. 
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... (SE)[*]
While predicting call rates, we call the external factors as "Special Events" (SE). 
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... rate[*]
In vector predictions that is an average call rate $Z_{p(i)}$. 
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... situation[*]
That means, there exist periods in the data file, with the identical combinations of impacts. Besides, these combinations are the same as that of the new and the present periods. 
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... available[*]
If a pair of periods, identical to the pair of the present and the next one, can be found. 
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... prediction"[*]
In section 10 the terms "one-step" and "multi-step" were used instead of "scalar" and "vector." 
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... Monday[*]
The complete list is $P$ for Monday, $A$ for Tuesday, $T$ for Wednesday, $K$ for Thursday, and $N$ for Friday. 
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... gaps[*]
A number of gaps in the current schedule $Mokytojai0$. 
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... class"[*]
A gap class is the class in the teacher gap. 
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... one[*]
An open class is the first or the last class for this teacher. 
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... too[*]
The optimization results depend on the initial schedules because there is no possibility to obtain exact solutions in a limited time. 
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... teachers[*]
If a teacher covers several subjects then he/she is represented as several different "virtual" teachers, feasibility conditions prevents cases with two or more lessons by the same "physical" teachers at the same time. 
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...#tex2html_wrap_inline15628#[*]
If the subject $n$ is covered by just one teacher $i$, then $n=1$. 
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... class[*]
This is a normative constraint, because several lessons may be performed in one class room, physically. 
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... lessons[*]
This means two lessons in a raw. 
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... groom[*]
By the "successful groom" we mean the groom that a bride marries. 
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... stage[*]
The meaning of the argument $q$ of the function $u_N(q)$ is defined by the index $N$, for example, $q=q_{N-1}$, if this index is $N$, etc. 
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