Necessary and sufficient

A living organism at any moment in its life is the unique consequence of a development history that results from the interaction of and determination by internal and external forces. The external forces, what we usually think as environment , are themselves partly a consequence of the activities of the organism itself as it produces and consumes the conditions of its own existence. 

We go back now to the question of whether and to what extent autopoiesis is the necessary and sufficient condition for cellular life. In the early days of autopoiesis, Maturana and Varela explicitly wrote (Maturana and Varela, 1980, p. 82) that autopoiesis is necessary and sufficient to characterize the organization of living systems and Gail Fleischaker, in the previously cited review on autopoiesis 

As a matter of fact, accephng the two assertions in the primary literature, one that autopoiesis is sufficient to characterize the organization of hfe, and the other, that cognition is equivalent to life, the conclusion should be reached that each autopoietic system is cognitive, and therefore living. This is actually what Heischacker refers to. 

I believe, however, that the assertion that every autopoietic system is living goes too far and in this section I would like to clarify the limits of this assertion. In doing so, I follow the lines of a paper recently presented in collaboration with Michel Bitbol (Bitbol and Luisi, 2004). The queshon of whether autopoiesis is the necessary and sufficient condition, or only the necessary one, has also been asked by Bourgine and Stewart, (2004) and earlier, in another context, by Weber (2002). 

To clarify this point, it may be useful to keep in mind two practical cases, which have been mentioned previously a synthetic vesicle that absorbs a particular molecule from the medium, and by so doing, reproduces itself via an autocatalytic process and - second case - a bacterium that recognizes and absorbs sugar from the environment. At hrst sight, these two processes are similar however, we would commonly ascribe the dehnition of living to the bacterium, and generally not to the other case. Intuitively, the difference can be seen in terms of cognition. How can we clarify this point  

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These rules are both necessary and sufficient to ensure that the target is achieved, providing the initialization rule is adhered to that no individual heat exchanger should have a temperature difference smaller than... 

Smith B.D. Image reconstruction from cone-beam projections necessary and sufficient conditions and reconstruction methods., IEEE Trans. Med. Imaging, V. 4, 1985, p. 14-28. 

As described earlier, translation of the EPSPS mRNA of plants results in the formation of a protein which has an AJ-terminal extension. The AJ-terminal extension, referred to as the chloroplast transit peptide, is necessary and sufficient for the import of the preprotein by the chloroplast. Once imported by the chloroplast, the transit peptide is cleaved releasing the mature enzyme. As expected, introduction of the EPSPS transit peptide to other protein sequences results in the importation of the fusion protein by the chloroplast. 

The immediate causes of the TOP event are shown in the fault tree with thek relationship to the TOP event. If any one of the immediate causes results dkecdy in the TOP event, the causes are connected to the TOP event with an OR logic gate. If all the immediate causes are requked for TOP event occurrence, then the causes are connected to the TOP event with an AND logic gate. Each of the immediate causes is then treated in the same manner as the TOP event, and its immediate, necessary, and sufficient causes are determined and shown on the fault tree with the appropriate logic gate. This development continues until all intermediate fault events have been developed into thek basic causes. 

Theorem 5. The transpose of is a complete B-matrrx of equation 13. It is advantageous if the dependent variables or the variables that can be regulated each occur in only one dimensionless product, so that a functional relationship among these dimensionless products may be most easily determined (8). For example, if a velocity is easily varied experimentally, then the velocity should occur in only one of the independent dimensionless variables (products). In other words, it is sometimes desirable to have certain specified variables, each of which occurs in one and only one of the B-vectors. The following theorem gives a necessary and sufficient condition for the existence of such a complete B-matrix. This result can be used to enumerate such a B-matrix without the necessity of exhausting all possibilities by linear combinations. 

If (a) above is satisfied, then the necessary and sufficient condition for stability is either... 

As the diagram develops, a necessary and sufficient test is applied to pairs of events, and checks for completeness and sequencing are made. One-to-many and many-to-one relations can be represented in the diagram. If data cannot be foimd to verify the relation between an event pair, then a technique called back-STEP can be used to explore gaps in understanding. Essentially back-STEP is a fault tree which uses the event with no other events leading to it as the top node. The analyst then develops possible event flows which could describe what happened during the gap in events in order to cause the top node. 

As the diagram develops, a necessary and sufficient test is applied to event pairs. For example, the event involving the night shift controller switching from pump B to pump A and the tripping of pump B are necessary for the... 

The following theorem - stated without proof (see [jen86a]) - gives necessary and sufficient conditions for CA rules to generate constant temporal sequences ... 

It should be emphasized that not all normalizable hermitean matrices r(x x 2. . . x xlx2. . . xp) having the correct antisymmetry property are necessarily strict density matrices, i.e., are derivable from a wave function W. For instance, for p — N, it is a necessary and sufficient condition that the matrix JT is idempotent, so that r2 = r, Tr (JH) = 1. This means that the F-space goes conceptually outside the -space, which it fully contains. The relation IV. 5 has apparently a meaning within the entire jT-space, independent of whether T is connected with a wave function or not. The question is only which restrictions one has to impose on r in order to secure the validity of the inequality... 

We conclude this section by deriving an important property of jointly gaussian random variables namely, the fact that a necessary and sufficient condition for a group of jointly gaussian random variables 9i>- >< to be statistically independent is that E[cpjCpk] = j k. Stated in other words, linearly independent (uncorrelated),46 gaussian random variables are statistically independent. This statement is not necessarily true for non-gaussian random variables. 

It is possible, of course, to use some sort of blank symbol to separate code words, but this would really imply that a tertiary alphabet was available. One easy way to guarantee that the code words can be separated from each other is to use a prefix code. We define a prefix code as a code in which no code word is the same as the initial part, or prefix, of another code word. More precisely, for any i and j, if % < np then vt must not be equal to the first nt digits of v. The following theorem now gives necessary and sufficient conditions on the set of lengths %, , n that can be used in a prefix code. 

Theorem 4-4 (Szilard, Kraft). A necessary and sufficient condition on the lengths n, 1 < j J, of the J code words of a binary prefix code is that... 

Poincar6-Bendixson (P.B.) Theorem.—This theorem gives the necessary and sufficient conditions for the existence of a cycle. Unfortunately, it requires a preliminary knowledge of the character of integral curves, which often makes its application difficult. The theorem states ... 

This condition is thus the necessary and sufficient condition for the existence of a stable stationary solution (oscillation) of the differential equation (6-127). 

Clearly for a vector ( ) to be transversal it is necessary and sufficient that at = 0. These transversal vectors lie in a hyperplane that is tangent to the light cone along ku. For a transversal vector one now verifies that... 

For the equilibrium of an isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy the variation of its entropy shall either vanish or be negative. 

The magnitude on the left is the heat absorbed in the isothermal change, and of the two expressions on the right the first is dependent only on the initial and final states, and may be called the compensated heat, whilst the second depends on the path, is always negative, except in the limiting case of reversibility, and may be called the uncompensated heat. From (3) we can derive the necessary and sufficient condition of equilibrium in a system at constant temperature. 

The necessary and sufficient criterion of equilibrium in a mechanically isolated system at a given temperature is ... 

Hence, for equilibrium in a system maintained at constant temperature and with constant external forces, it is necessary and sufficient that for all virtual changes ... 

If the only external force is a normal, uniform, and constant pressure p, the necessary and sufficient condition for equilibrium is that for all virtual isothermal-isopiestic changes ... 

The necessary (and sufficient) condition for a three-dimensional Pfaffian to be inexact but integrable is... 

These boundary conditions are necessary and sufficient for the solution of equation 10.100 which is first order with respect to f and second order with respect to y. 

The translational periodicity of the potential is the necessary and sufficient condition for describing the wavefunction as a linear combination of Bloch functions... 

Difference equations with a symmetric matrix are typical in numerical solution of boundary-value problems associated with self-adjoint differential equations of second order. In what follows we will show that the condition Bi = is necessary and sufficient for the operator [yj] be self-adjoint. As can readily be observed, any difference equation of the form... 

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