spines (figs. 10, 11, 12, q). Besides double tentacle hooks, there are others that are simple, and, from the grain on which they are mounted as a base, may be termed grain hooks. Those that first appear are simple spicules, bent or straight, standing on the side arm plates, above the tentacle hooks (figs. 8, 9). Then a granule is formed under them (fig. 13). More of such hooks grow on the grains or little swollen plates which occupy the position of upper arm plates among Ophiurans (fig. 10). Later there remain on the side arm plate only the true tentacle hooks, while the grain hooks stand on those double rows of raised grains which give the ringed or burr look to the small branches of Astrophytons (Pl. XXXV. fig. 19). As they approach the disk and thicker part of the arm these raised rows sink and their hooks disappear, and a coarse granulation overgrows the first layer of swelled plates, so that the surface of the arm becomes even. The side arm plates which began as ridges encircling the whole arm change their character rapidly. In the central depression between them, on the upper side of arm, a little upper arm plate begins to form (Pl. XXXVI. fig. 5), like a perforated lime crust. Then, as the arm enlarges, the side plates separate above, and between them are formed additional scales, which occupy the position of upper arm plates, but follow no rule in their growth (fig. 7). They do not even multiply by the irregular method of *Hemieuryale pustulata.* These scales, at first thin (figs. 7, 15), afterwards thicken and become more rounded (figs. 10, 11), and some of them make the basis of the two annular rings of grains carrying the grain hooks, which afterwards drop off, so that at the base of an arm there appear (in a dry specimen) only the thickened skin, with a granular coat and a few irregular plates above the side arm plates. These last, early separated above (figs. 7, 13), maintain their union underneath (figs. 6, 12, 16, 17, 19, i). It follows that the growing arm rises more and more above them. They retain their simple form almost throughout, but, within the disk, in fully grown specimens they are broken in two (fig. 19, i). The under arm plates first appear about two forks from the tip of the arm; not, however, simple, but divided in three parts (fig. 12, h), which may still be seen inside the disk of young specimens (fig. 17, h, h). In adults these plates, at the third fork of the arm, are in four triangular pieces, making together an oblong figure. Within the disk the number of pieces is considerable and their form irregular (fig. 19). In this respect there is a marked difference from Ophiurans, whose upper arm plates may be composed of several pieces developed under certain rules, but whose side and under plates are almost always simple, rarely of two pieces, and in one species only (*Ophiomyxa pentagona*) of three pieces.

2 Lütken's figures indicate that the young of *Gorgonocephalus cucematus* has the under arm plate not divided (Addit. ad Hist. Oph., vol. i., pl. ii. figs. 17b and 17d).
The skeleton of a *Gorgonocephalus* does not differ more from that of an ordinary Ophiuran than those of Ophiurans differ among themselves. All the mouth parts are present (figs. 18, 19); mouth frames (*f*), jaws (*c*), jaw plate (*e*), sockets for two sets of tentacles (*r, r'*), and a large peristomial plate (*v*) in two pieces. There is, in addition, a small angle cover (*v'*), which is strongly developed in most Astrophytous, and which Ludwig considers the first under arm plate. The radial shield, genital plate (*o*), and genital scale (fig. 17, *n*) occupy normal positions. In regard to the radial shields, this peculiarity is to be remarked, that they are made up of a series of plates soldered one on the other like tiles. This structure calls attention to the fact that radial shields, which, from their almost constant presence, and their articulation with the genital plate, are usually considered exceptional parts, are truly nothing more than a disk scale, or a series of soldered disk scales. Hinged to the genital plates they regulate the position of the roof of the disk as it is raised or lowered. Moreover, the genital plates themselves, with their genital scales, are nothing more than highly specialised scales of the lower interbrachial space, folded in, and bounding the genital openings on either side. In some genera (*e.g.*, *Ophiomusium*) the genital plate is externally conspicuous as one of the chief pieces of the lower interbrachial space. The arm bones do not essentially differ from those of Ophiurans, except that their joints are simplified so as to be adapted to rolling in a vertical plane. The outer face has the usual transverse hour-glass projection, which is vertical on the inner face.

Passing now to *Euryale*, striking variations present themselves. The proportions and arrangement of the mouth differ much from those of *Gorgonocephalus*. Two large, flattened jaws (Pl. XXXV. fig. 1, *c*) support a small jaw plate (*e*), which carries, not the usual bunch of spines, but a vertical row of flat teeth (*d'*) like those of Ophiurans, or those of *Astroschema*. Seen from above, the jaws (*e*) and mouth frames (*f*) are much more solid than in *Gorgonocephalus*, and the peristomial plate (*v*), instead of being flat and divided, is much swollen and single. While *Gorgonocephalus* has the under arm plates in three pieces at the tip of the arm, and existing at its base only as irregular, broken scales, *Euryale* has them nearly or quite unbroken (figs. 1, 6, *h*) and of a regular form for the whole length of the arm except the terminal twigs. It is at the end of the arm that there is a remarkable difference in the side plates of the two genera. *Gorgonocephalus* has small thick plates clinging close to the arm, while *Euryale* is furnished with long, finger-like projections standing free and bearing prehensile hooks (figs. 8–12).

A side arm plate of the same general character may be found at the tip of the arm of *Ophiiothrix pusilla*. Passing towards the disk, these plates grow shorter and wider, and their hooks thicken into club spines (figs. 8, 9, *i, j*). Still further inward the side plates are nearly like those of Ophiurans, and carry little conical tentacle scales (or arm spines) on

---

The exterior double rows of hook-bearing grains, found in *Astrophyton, Gorgonocephalus, Astroclon, Astrocnida, Astroporpa, Astrogomphus, Astrochele, and Astrotoma* do not exist at all in this genus, which agrees in this respect with *Trichaster, Astroceras, Astroschema, Ophiocreas*, and *Astronyx*. The chief bracing pieces, namely, radial shield and genital plate, are stout and firmly hinged, and the former (fig. 3, 1), instead of being composed of united overlapping scales, is solid; while the latter (α) is firmly bedded in a series of soldered plates, which connect it with the side arm plates (i). Attached to the articulation is a short, very stout, genital scale (α). The arm bones are lower and wider than among kindred genera, but are jointed in the usual way; that is to say, the inner face presents a vertical prominence constricted in the middle (fig. 14, β), while the outer face has a similar but horizontal prominence (fig. 13, γ), and the two, held together by muscles and skin, make a free-playing joint. At each forking of the arm a curious modification takes place. The bone, while retaining its general form, is much widened and is split vertically almost in two (fig. 16); on the inner face of each half is a vertical hour-glass prominence (β), and the outer face of the arm bone next within is suitably modified (fig. 15) by being much widened, and by having, at its constricted part, an articulating peg, or wedge, which fits into the hollow between the two vertical hour-glasses just described. At the joint outside these, the forking is perfect, and each prong has an arm bone of nearly the normal shape.

**Table of Species of *Astrophyton*.**

Description
Species

Disk with very high radial shields bearing a few stout stumps, covered
Astrophyton costatum.</


intrinsic pedal muscles in this animal are well represented. The dorsal layer is very deficient.

_Plantar layer._—In this group there are three muscles, viz. :-

1. Adductor hallucis.
2. Adductor indicis.
3. Adductor minimi digiti.

They all arise by a common origin from the middle of the plantar surface of the tarsus, and, separating, they radiate from each other to reach their insertions. The adductor hallucis is inserted into the extensor tendon upon the outer side of the base of the hallux; the adductor indicis into the extensor tendon upon the same aspect of the base of the index; and the adductor minimi digiti into the extensor tendon upon the inner aspect of the base of the first phalanx of the minimus.

_Intermediate layer._—As in the Beaver, the index, medius, and annularis have each a two-headed flexor brevis. This muscle springs from the base of the corresponding metatarsal, and its two heads, embracing the root of the toe with which it is connected, are inserted partly into the sesamoid and partly into the extensor tendon.

The flexor brevis minimi digiti has only a fibular head. This is a stout, fleshy belly which springs from the under surface of the external cuneiform bone, and is inserted into the outer sesamoid of the minimus.

The flexor brevis hallucis is represented by a tibial head which is much smaller than the preceding muscle. It arises from the under surface of the scaphoid, and is inserted upon the inner side of the first phalanx of the hallux.

_Dorsal layer._—This layer is poorly developed. It has the following components :—

1. The abductor hallucis.
2. The second and fourth dorsal interossei.
3. The abductor ossis metatarsi minimi digiti.
The abductor hallucis is exceedingly small and closely applied to the tibial head of the flexor brevis hallucis. In great part fibrous, it arises from the scaphoid, and is inserted upon the inner side of the nodular first phalanx of the hallux.

The second and fourth dorsal interossei are strong, single-headed muscles which act as abductors of the index and annularis from the middle toe. There is no trace to be found of the other two interosseous muscles.

The abductor ossis metatarsi minimi digiti hardly deserves the name of a muscle. It is merely a stout fibrous band with an admixture of fleshy fibres which presents the attachments of this muscle.

Nervous arrangements.—The intrinsic muscles are supplied in the usual manner—the abductor and flexor brevis hallucis by the internal plantar nerve; the others by the external plantar. It is to be noted that the deep division of the latter nerve crosses the foot subjacent to the plantar muscles, and that it gives off the digital branch for the adjacent sides of the annularis and minimus. This branch reaches its destination by emerging from under cover of the adductor minimi digitii.

A comparison of the feet of the foregoing members of the Rodent order shows what seems to be a tendency to the disappearance of the plantar and dorsal muscles, but a retention of the intermediate muscles. The following table renders this evident:

### Plantar layer.

Animal
Adductors

Paca
Three strongly developed adductors.

Hare
Two feeble adductors.

Beaver
One very weak adductor (with traces of a second).

Bathyergus
None.

Cape Mouse

### Dorsal layer.

Animal
Members of this group

Paca
Four members of this group (two very weak).

Beaver
Four members of this group (one very weak).

Hare
None.

Bathyergus

Cape Mouse

### Intermediate layer.

Animal
Members of this group

Bathyergus
Five members of this group.

Paca

Hare
Four members of this group.

Beaver
Three members of this group (with traces of two others).

Further, according to St. George Mivart and Murie,¹ we may class with the Bathy-

ergus and Cape Mouse the Crested Agouti and the Guinea Pig, in both of which flexores breves are alone developed.

Cheiroptera.

Pteropus (Fox-bat), (Pl. XI. figs. 1 and 2).

The foot of the Fox-bat is pentadactylous—the four outer toes being of nearly equal length, and the hallux slightly smaller. All the digits are armed with sharp curved claws. The intrinsic muscles are well marked, but the dorsal or abducting members of the group, with one exception, are absent. They are all placed upon the plantar aspect of the metatarsus, and are all but invisible from the dorsal aspect of the foot.

Plantar layer.—Only two muscles of this layer are represented, viz.:

1. Adductor hallucis (p¹).
2. Adductor minimi digiti (p²).

These muscles together form a thin triangular sheet of muscular fibres spread out upon the flexores breves, but separated from them by the deep division of the external plantar nerve (d.d). This muscular sheet arises by its apex from the plantar surface of the tarsus somewhat nearer the inner than the outer margin of the foot, and it is mapped out into the two adducting muscles by a distinct fibrous raphe which extends from the apex to the base. The distal end of the raphe is not attached, and ends close to the inner side of the root of the medius. The adductor minimi digiti is much the larger of the two muscles, and is inserted into the inner sesamoid at the base of the first phalanx of the minimus. The adductor hallucis, small in proportion to the preceding, is inserted into the outer sesamoid at the base of the first phalanx of the hallux.

Intermediate layer.—This layer is typically complete (f¹ to f⁵). A flexor brevis is provided for each digit; each muscle consists of two heads, and these are separate throughout their entire length. This group therefore is composed of eight distinct muscular slips, all of which lie upon the same plane. They arise from the fibrous textures at the base of the metatarsus and are inserted into the sesamoid bones alone.

The outer head of the flexor brevis minimi digiti, and the inner head of the flexor brevis hallucis, are considerably larger than the others. This increase in bulk may be due to their having coalesced with the absent abductor minimi digiti, and abductor hallucis.

Dorsal layer.—The only member of this layer which is present is the abductor ossis metatarsi minimi digiti (d⁵). It is well developed, and has the usual connections. Not a trace of the dorsal interossei is to be found.

Nervous arrangements.—The posterior tibial nerve divides into its two terminal branches in the hollow of the os calcis.
The internal plantar nerve (i.p.n) on entering the sole at once breaks up into four
digital branches:—These are distributed as follows:—(1) the innermost goes to the inner
side of the hallux and gives three minute twigs to the large inner head of the flexor brevis
hallucis; (2) the next divides to supply the adjoining margins of the hallux and index,
and gives a muscular twig to the first lumbral; (3) the third bifurcates and supplies
the adjacent borders of the index and medius, and furnishes a filament to the second
lumbral; (4) the fourth in like manner supplies the contiguous sides of the medius and
annularis, and gives a twig to the third lumbral. From the trunk of the internal
plantar, before it breaks up into its digital branches, a few filaments are furnished to
the flexor brevis digitorum.

The external plantar nerve (e.p.n) turns outwards under cover of the flexor brevis
digitorum, and after supplying the abductor ossis metatarsi minimi digiti with one or
two twigs divides into its superficial and deep divisions. The superficial part ends in
two digital branches, of


 upland movement habitat and 6,783 acres of overwintering habitat.

Activities under the conservation strategy that require ground or vegetation disturbance could result in adverse effects on this species. In addition to management activities under the conservation strategy, the Neighboring Land Owner Program provides take coverage for giant garter snake on private lands adjacent to reserve system lands as discussed above and in Section 2.3.2, Alternative B—Proposed Action Alternative (Permit Issuance/Plan Implementation).

Projects and activities under the Proposed Action Alternative, including conservation strategy activities that have the potential to result in giant garter snake habitat loss and/or mortality, would be required to implement general project and construction AMMs as discussed above to reduce these effects to the greatest extent practicable. In addition to these general project and construction AMMs, covered activities would be required to implement an AMM specific to the avoidance and minimization of take of giant garter snake. This species specific AMM is shown in Table 2-7 and detailed in Appendix C. This AMM requires avoidance of development in or within 200 feet of aquatic habitat, and if habitat cannot be avoided survey using the USFWS protocol (USFWS 1997), as well as additional measures to encourage giant garter snakes to leave the site on their own accord, and measures to avoid injury or mortality if giant garter snakes are encountered during construction.

The conservation strategy includes a monitoring and adaptive management component as well as the incorporation of 2,910 acres of giant garter snake habitat on pre-permit reserve lands, and specific biological objectives for the conservation of giant garter snake including; protecting 2,800 acres of rice fields, 1,160 acres of upland habitat, 500 acres of emergent wetland, and 420 acres of lacustrine and riverine suitable habitat for giant garter snake. The conservation strategy also prioritizes the incorporation of lands into the reserve system that are adjacent to existing conservation lands will further limit the effects on the species from habitat fragmentation [See Section 2.3.2, Alternative B—Proposed Action Alternative (Permit Issuance/Plan Implementation)].

As the result of the conservation strategy, a total of 10,290 acres of giant garter snake would be protected, monitored and adaptively managed. In addition, the connectivity of habitat, as well as monitoring and adaptive management under the conservation strategy would provide additional value beyond the project by project mitigation that would occur under the No Action Alternative.

Conservation activities under the Proposed Action Alternative are similar to those that would be required by the permitting process under the No Action Alternative. The conservation strategy is also expected to result in additional benefits to the species above what would likely be required under the No Action Alternative. This would result, in part, through the inclusion of habitat in a reserve system that incorporates and is
connected to baseline public and easement lands and is subject to monitoring and adaptive management, which would not be required under the No Action Alternative which does not include one cohesive conservation strategy. In addition, all covered activities would be subject to general and species specific AMMs that would further reduce adverse effects on giant garter snake. However, take granted through the neighboring landowner protection program could reduce the beneficial effects of the conservation strategy.

**NEPA Level of Significance:** As compared to the No Action Alternative, this impact is **beneficial**.

**CEQA Level of Significance:** As compared to Existing Conditions, this impact is **less than significant** as implementation of the conservation strategy results in the minimization of effects on this species and compensation for effects that cannot be fully avoided.

*No mitigation is required.*

**Effect Bio-6: Swainson’s hawk.**

Swainson’s hawk is proposed for coverage under the Yolo HCP/NCCP and is listed as a Bird of Conservation Concern by the USFWS and as threatened under CESA. Swainson’s hawk is a seasonal resident of the Plan Area and is generally present from early March, to occupy previous nesting territories or establish new territories, until October, when young have fledged and fall migration is complete. Nesting habitat is predominately within natural riparian woodlands, though trees may be used in other natural and developed habitat types. Foraging habitat consists of natural grassland and agricultural land types that provide similar low open vegetation and high rodent densities (e.g., alfalfa, dry grain and row crops). A complete description of modeled Swainson’s hawk habitat, a detailed species account, and a list of occurrences in the Plan Area can be found in Appendix D. There are 15,673 acres of nesting habitat, 534 nesting sites, 79,336 acres of natural foraging habitat, and 214,078 acres of cultivated lands foraging habitat in the Plan Area.

Activities under the conservation strategy that require ground or vegetation disturbance could result in adverse effects on this species. Projects and activities under the Proposed Action Alternative, including conservation strategy activities that have the potential to result in Swainson’s hawk habitat loss and/or mortality, would be required to implement general project and construction AMMs (as discussed above in the analysis of the Proposed Action Alternative), to reduce these effects to the greatest extent practicable. In addition to these general project and construction AMMs, covered activities would be required to implement an AMM specific to the avoidance and minimization of take on Swainson’s hawk and white-tailed kite. This species specific AMM is detailed in Appendix C and requires avoidance of nest trees, or implementation of surveys for active nests as outlined by Swainson’s Hawk Technical Advisory Committee (2000) and buffers around active nests. This AMM does allow for the removal of up to 20 nest trees (documented nesting within last 5 years) over the permit term, but not while occupied during the nesting season.

The conservation strategy includes a monitoring and adaptive management component as well as the incorporation of 4,795 acres of Swainson’s hawk habitat on pre-permit reserve lands, and biological objectives for the conservation of Swainson’s hawk including; maintaining crop types that support Swainson’s hawk habitat within the 14,362 acres of protected agricultural lands, provide 4,430 acres of natural foraging habitat, protect and maintain at least 40 protected nest trees, and maintain a density of one suitable nest tree per 10 acres of agricultural lands in the reserve system. The conservation strategy also prioritizes the incorporation of lands into the reserve system that are adjacent to existing conservation lands, which would further limit the effects on the species from habitat fragmentation [See Section 2.3.2, Alternative B—Proposed Action Alternative (Permit Issuance/Plan Implementation)]. As the result of the conservation strategy, at total of 26,031 acres of Swainson’s hawk habitat would be protected, monitored and adaptively managed.

Conservation activities under the Proposed Action Alternative are similar to those that would be required by the permitting process under the No Action Alternative. The conservation strategy is also expected to result in additional benefits to the species above what would likely be required under the No Action Alternative. This would result, in part, through the inclusion of habitat in a reserve system that incorporates and is connected to baseline public and easement lands and is subject to monitoring and adaptive management,
which would not be required under the No Action Alternative which does not include one cohesive conservation strategy. In addition, all covered activities would be subject to general and species specific AMMs that would further reduce adverse effects on Swainson’s hawk.

**NEPA Level of Significance:** As compared to the No Action Alternative, this impact is **beneficial**.

**CEQA Level of Significance:** As compared to Existing Conditions, this impact is **less than significant** as implementation of the conservation strategy results in the minimization of effects on this species and compensation for effects that cannot be fully avoided.

*No mitigation is required.*

**Effect Bio-7: White-tailed kite.**

White-tailed kite is proposed for coverage under the Yolo HCP/NCCP and is a California fully protected species and protected under the MBTA. White-tailed kite is a year-round resident of the Plan Area that has similar nesting habitat to that described for Swainson’s hawk though the species exhibits less of a preference for a specific vegetation type. Foraging habitat is also similar to that of Swainson’s hawk, though defined for the purpose of this analysis as more frequently used primary and less frequently used secondary foraging habitat. A complete description of modeled white-tailed kite habitat, a detailed species account, and a list of occurrences in the Plan Area can be found in Appendix D. There are 31,732 acres of nesting habitat, 531 nesting sites, 101,758 acres of primary foraging habitat, and 134,740 acres of secondary foraging habitat in the Plan Area.

Activities under the conservation strategy that require ground or vegetation disturbance could result in adverse effects on this species. Projects and activities under the Proposed Action Alternative, including conservation strategy activities that have the potential to result in white-tailed kite habitat loss and/or mortality would be required to implement general project and construction AMMs and the same species specific AMMs as discussed above for Swainson’s hawk.

The conservation strategy includes a monitoring and adaptive management component as well as the incorporation of 3,545 acres of white-tailed kite habitat on pre-permit reserve lands. There are no specific biological objectives for the conservation of white-tailed kite, though the natural community objectives related to its habitat provide conservation for the species. The conservation strategy also prioritizes the incorporation of lands into the reserve system that are adjacent to existing conservation lands will further limit the effects on the species from habitat fragmentation


/[T, T] \cong C_2 \times C_4$ by the above description of $T/E$ (where $E \leq [T, T]$), $\text{Aut}(T)$ and hence $\text{Out}_\text{typ}(L)$ are 2-groups. So each automorphism of the amalgam $H > T < N$ determines a larger amalgam. Since the only extension of this amalgam is to that of $^2F_4(2)$ by [Fn, Theorem 1], $|\text{Out}_\text{typ}(L)| = 2$. □
5. The cross characteristic case: I

Throughout this section, we will work with groups \( G = C_G(\sigma) \) which satisfy the conditions in Hypotheses 5.1 below. In particular, 5.1(1) implies that \( G \) is not a Suzuki or Ree group. We will see in Section 6 (Proposition 6.8) that while these hypotheses are far from including all finite Chevalley and Steinberg groups, their fusion systems at the prime \( p \) do include almost all of those we need to consider.

For any finite abelian group \( B \), we denote its “scalar automorphisms” by
\[
\psi^B_k \in \text{Aut}(B), \quad \psi^B_k(g) = g^k \quad \text{for all } k \text{ such that } (k, |B|) = 1
\]
and define the group of its scalar automorphisms
\[
\text{Aut}_{sc}(B) = \{ \psi^B_k \mid (k, |B|) = 1 \} \leq Z(\text{Aut}(B)).
\]

**Hypotheses 5.1.** Assume we are in the situation of Notation 2.2(A,B,C).

(I) Let \( p \) be a prime distinct from \( q_0 \) such that \( p | W_0 | \). Assume also that \( \sigma = \psi_q \circ \gamma = \gamma \circ \psi_q \in \text{End}(\overline{G}) \), where

- \( q \) is a power of the prime \( q_0 \);
- \( \psi_q \in K_G \) is the field automorphism (see Definition 3.1(a)); and
- \( \gamma \in \text{Aut}(\overline{G}) \) is an algebraic automorphism of finite order which sends \( \overline{T} \) to itself and commutes with \( \psi_{q_0} \) (so that \( \psi_{q_0}(G) = G \)).

Also, there is a free (\( \tau \))-orbit of the form \( \{\alpha_1, \alpha_2, \ldots, \alpha_s\} \) or \( \{\pm \alpha_1, \pm \alpha_2, \ldots, \pm \alpha_s\} \) in \( \Sigma \) such that the set \( \{\alpha_1, \alpha_2, \ldots, \alpha_s\} \) is linearly independent in \( V \).

(II) The algebraic group \( \overline{G} \) is of universal type, and \( N_G(T) \) contains a Sylow \( p \)-subgroup of \( G \).

(III) Set \( A = O_p(T) \). Assume one of the following holds: either

(III.1) \( q \equiv 1 \pmod{p} \), \( q \equiv 1 \pmod{4} \) if \( p = 2 \), \( |\gamma| \leq 2 \), and \( \gamma \in \Gamma_{\overline{G}} \) (thus \( \rho(\Pi) = \Pi \)); or

(III.2) \( p \) is odd, \( q \equiv -1 \pmod{p} \), \( G \) is a Chevalley group (i.e., \( \gamma \in \text{Inn}(\overline{G}) \)), and \( \gamma(t) = t^{-1} \) for each \( t \in \overline{T} \); or

(III.3) \( p \) is odd, \( |\tau| = \text{ord}_p(q) \geq 2 \), \( C_A(O_{p'}(W_0)) = 1 \), \( C_S(\Omega_1(A)) = A \), \( \text{Aut}_G(A) = \text{Aut}_{W_0}(A) \),

\[
N_{\text{Aut}(A)}(\text{Aut}_{W_0}(A)) \leq \text{Aut}_{sc}(A) \text{Aut}_{\text{Aut}(G)}(A)
\]

where \( \text{Aut}_{\text{Aut}(G)}(A) = \{ \delta | A \mid \delta \in \text{Aut}(G), \delta(A) = A \} \), and

\[
\text{Aut}_{W_0}(A) \cap \text{Aut}_{sc}(A) \leq \begin{cases}
\langle \gamma | A \rangle & \text{if } 2 | \text{ord}_p(q) \text{ or } -\text{Id} \notin W \\
\langle \gamma | A, \psi_{\overline{A}} \rangle & \text{otherwise},
\end{cases}
\]

Since \( W_0 \) acts on \( T \) by Lemma 2.3, it also acts on \( A = O_p(T) \).

We will see in Lemma 5.3 that the conditions \( C_S(\Omega_1(A)) = A \) (or \( C_S(A) = A \) when \( p = 2 \)) and \( \text{Aut}_G(A) = \text{Aut}_{W_0}(A) \), both assumed here in (III.3), also hold in cases (III.1) and (III.2).

Recall, in the situation of (III.3), that \( |\tau| = |\gamma|_{\overline{\gamma}} \) by Lemma 3.2.

Note that the above hypotheses eliminate the possibility that \( G \) be a Suzuki or Ree group. Since we always assume the Sylow \( p \)-subgroups are nonabelian, the only such case which
needs to be considered here (when \( q_0 \neq p \)) is that of \( {}^2F_4(q) \) when \( p = 3 \), and this will be handled separately.

By Lemma 3.2, whenever \( \sigma = \psi_q \circ \gamma \), and \( \gamma \) is an algebraic automorphism of \( \bar{G} \) which normalizes \( \bar{T} \), there is \( \tau \in \text{Aut}(V) \) such that \( \tau(\Sigma) = \Sigma \) and \( \sigma(\bar{X}_\alpha) = \bar{X}_{\tau(\alpha)} \) for each \( \alpha \in \Sigma \). So under Hypotheses 5.1, the condition at the beginning of Notation 2.2(C) holds automatically, and with \( \rho = \tau|_\Sigma \). To simplify the notation, throughout this section and the next, we write \( \tau = \rho \) to denote this induced permutation of \( \Sigma \).

The following notation will be used throughout this section, in addition to that in Notation 2.2. Note that \( \hat{\Pi} \) and \( \hat{\Sigma} \) are defined in Notation 2.2(C) only when \( \rho(\Pi) = \Pi \), and hence only in case (III.1) of Hypotheses 5.1. It will be convenient, in some of the proofs in this section, to extend this definition to case (III.2).

Recall (Notation 2.2) that for \( \alpha \in \Sigma \), \( w_\alpha \in W \) denotes the reflection in the hyperplane \( \alpha^\perp \subseteq V \).

**Notation 5.2.** Assume we are in the situation of Notation 2.2 and Hypotheses 5.1.

(D) If (III.2) holds, then set \( \hat{\Sigma} = \Sigma \), \( \hat{\Pi} = \Pi \), and \( V_0 = V \). Note that \( W_0 = W \) in this case.

(E) If (III.1) holds, then for each \( \hat{\alpha} \in \hat{\Sigma} \), let \( w_{\hat{\alpha}} \in W_0 \) be the element in \( \langle w_\alpha \mid \alpha \in \hat{\alpha} \rangle \) which acts on \( V_0 \) as the reflection across the hyperplane \( \langle \hat{\alpha} \rangle^\perp \), and which exchanges the positive and negative roots in the set \( \langle \hat{\alpha} \


 supersonic flow and high speed Schlieren photographs were taken. These photographs revealed a highly unstable shock pattern ahead of the canopy. Similar tests of flexible models showed irregular oscillation, structural instability, and eventual destruction of the canopy.

The analysis of the conventional parachute in supersonic flow, and the subsequent development and testing of a supersonic retardation device proceed in the following phases:

1) Pressure distribution studies on conventional canopy in supersonic flow

2) Water analogy studies in conventional water tow

3) Water analogy studies in water table with stationary models

4) Wind tunnel stability studies of supersonic parachutes

5) Drag studies of supersonic parachutes.

These phases will be reported in respective order in the following sections of this report.
5.2 Pressure Distribution Studies in Supersonic Wind Tunnel

5.2.1 As a first step in the analysis of conventional parachutes, the pressure distribution on both the inside and outside surfaces of a conventional ribbon parachute model suspended in the wake of an ogive cylinder forebody was studied. Model geometry, test arrangement, and pressure distribution for Mach numbers of 0.8, 1.2, and 4.5 were presented in Progress Report No 12. Pressure distributions for Mach 3.0 were given in Progress Report No 15.

5.2.2 During this reporting period, tests were made to determine the influence of the ogive-cylinder forebody on the internal and external pressure distributions on the canopy at Mach numbers of 1.08 and 3.0. These tests were made with and without suspension lines, in order to determine their effect on pressure distribution. Previously, the transonic tests were made at Mach 1.2; however, in the wind tunnel now being used, the highest attainable Mach number with the model mounted in the test section was Mach 1.08. Therefore, the transonic studies were continued at this Mach number.

5.2.3 The parachute models and testing procedure were the same as in previous studies. As before, two secondary parachute models were used, one to measure internal and the other to measure external pressures. The suspension lines for these tests were secured at the confluence point by a set of guy wires fastened to the tunnel walls (see Fig 7-1). The pressures were measured on a multiple manometer and photographed during each test. Three tests were conducted for each configuration at both Mach numbers.

5.2.4 Results
5.2.4.1 The pressure measurements from three internal and three external pressure distribution tests were averaged in each case. These measurements were then reduced to coefficient form with the pressure coefficient, \( C_p \), defined as

\[
C_p = \frac{P_L - P_s}{q},
\]

where

- \( P_L \) = local pressure on the surface of the model
- \( P_s \) = free stream static pressure
- \( q \) = free stream dynamic pressure.

5.2.4.2 Figures 7-2 and 7-3 present the pressure coefficient distribution of the parachute model in free stream with and without suspension lines, respectively, at transonic Mach numbers. For comparison, Fig 7-4 presents these two sets of curves together with the pressure distribution of the model with suspension lines behind an ogive-cylinder forebody (previously presented as Fig 7-11, Progress Report No 12). Similarly, Figs 7-5 through 7-7 present the same sequence of pressure coefficient distributions at Mach 3.0. It is seen that the forebody has only a small influence on either the internal or external pressure coefficient at Mach 1.08 and 3.0. The suspension lines do have noticeable influence on the magnitude of the internal pressure coefficient, especially at Mach 3.0. This increase in internal pressure coefficient is due to the large pressure recovery across the well defined shock ahead of the canopy without suspension lines (see Sec 5.2.4.3). The suspension lines do not noticeably influence the external pressure coefficient at either Mach number.
Figures 7-8 and 7-9 are double exposure shadowgraphs of the flow pattern at Mach 3.0 about a parachute model in free stream with and without suspension lines, respectively. It is seen that apparently the suspension lines cause a highly irregular shock pattern ahead of the canopy. In tests without suspension lines, a stable detached shock wave pattern is formed. However, this contradicts previous experience, and efforts are now being made to explain this contradiction, as outlined in Sec 5.2.5.1 below.

Proposed Work

The pressure distribution studies as specified in the present contract have been completed. However, during the next reporting period, additional wind tunnel tests of several canopies with varying porosities and different methods of mounting will be made to determine the factors which influence the character of the shock wave ahead of the canopy without suspension lines. These tests will be conducted at Mach numbers of 2.0 and 3.0.

During the next reporting period, work will begin on the writing of a final report for this phase of the project.

Water Tow Studies

As a second phase of the investigation, a series of two-dimensional water analogy studies have been made to visualize flow patterns within the canopy. These studies were applied first to the analysis of the instability of conventional parachutes, reported in Progress Report No 12, and later to stability studies of various configurations of the so-called spiked parachute, reported in the Supplement to Progress Report No 13.
5.3.2 During this reporting period, a series of tests was performed at Mach 2.0 with the spiked parachute behind an ogive-cylinder forebody with a caliber of 2.5. Tests were run at L/D ratios of 4.5 and 8. The ratio of the parachute model maximum diameter to the forebody diameter was 2.

5.3.3 Results

Figures 7-10 and 7-11 show the flow pattern about the spiked parachute behind the forebody (see Progress Report No 15, Fig 7-5, for identification of parameters). For comparison, Fig 7-12 shows the flow pattern about the model in free stream at Mach 2.0. It is seen that the flow patterns are somewhat less defined for the parachute in the wake of the forebody but similar in nature. The stability seems to be unaffected.

5.3.4 Proposed Work

Water analogy experiments will be continued in close coordination with supersonic wind tunnel tests of the spiked parachute. Making use of existing property analogies (derived in Progress Report No 1), attempts will be made to determine pressure distribution and relative drag of retardation devices in the water tow tank.

5.4 Stationary Model Water Analogy Studies

5.4.1 The advantages of complementing the conventional water tow experiments with studies in a moving water channel were enumerated in Progress Report No 15. Desirable features for the projected facility were indicated and the detail design was begun.

5.4.2 During this reporting period, the design of the main component
parts of the new water channel, including the structural framework and the water ducting and reservoir, was completed. Bids for the construction of these parts were received from local machine shops, but acceptance of a bid was delayed because of the termination of the present contract. Upon authorization in the new contract, a bid will be accepted.

5.4.3 A Description of the New Water Channel

5.4.3.1 Figure 7-13 is a general assembly drawing of the proposed facility, and shows the main features and dimensions. The main components will be described in the following paragraphs of this report.

5.4.3.2 Main Channel and Supporting Structure

The rectangular channel is approximately 20 ft long, 52 inches wide, and 5 inches deep. The channel floor consists of one piece of high grade, mirror finish plate glass 15 ft long and 3/4 inch thick. The glass rests on plexiglass support pads mounted on adjustable swivel screws used for fine adjustment in levelling the surface of the glass.

The vertical side walls of the channel are made of 6 x 3 1/2 x 3/8 inch right angle structural steel attached to the top chord of the supporting structure. The channel is supported by two parallel steel trusses 2 ft deep; its top chords consist of 4 x 2 1/4 inch steel channel sections running the entire length of the structure. The lower chord is made 4 ft shorter at the downstream end of the channel to provide space for the pump and motor drive. At 2 1/2 ft intervals, there are cross ties joining the two top and the two bottom chords. The swivel screws and plastic pads
which support the glass floor of the channel are screwed at intervals into the ties between the top chords. Ties at the lower panel joints support the water supply pipe and ducting. Horizontal diagonal bracing members were avoided in order to have large, unobstructed panels directly beneath the glass floor for photographic purposes.

5.4.3.3 Channel Tilting Mechanism

A uniform slope of the channel is necessary to secure uniform flow velocity. This slope must be adjustable in order to attain the water flow velocity representing a certain Mach number. Variation of the longitudinal slope of the channel is provided by means of the tilting mechanism illustrated in Fig 7-13. At the downstream end of the lower chord, the trusses are mounted on hinge pins. Near the upstream end of the channel, a 1 inch diameter bar is welded transversely to the bottom of the upper chord members. This bar will be carried by two hydraulic rams, one on each side. The hydraulic rams are connected to a hand operated hydraulic pump by means of flexible pressure tubing and shut-off valves. The hydraulic rams have


Division of Cancer Science and Molecular Pathology, Glasgow University, Western Infirmary (Pathology), Dumbarton Road, Glasgow G11 6NT, U.K.

Abstract

Mammalian erythrocytes are generally thought to lack RNA and therefore to be unable to translate new proteins in response to internal or external signals. Support for this long-standing view has accumulated from diverse studies, most of which have focused on the total content of RNA or the overall level of translation. However, more recent work on specific types of RNA has shown the presence in human erythrocytes of both Y RNA and microRNA. The latter seem particularly incongruous given that their normal role is to attenuate the translation of mRNA. Y RNA binds the Ro autoantigen which may have a role in cellular RNA quality control. Therefore the presence of both of these non-coding RNAs indicates the possible existence of other cryptic RNAs in erythrocytes. It also suggests either the existence of low levels of translation or new uncharacterized processes involving microRNA in these cells.

Erythrocyte biology

Vast numbers (~2–3×10¹³) of erythrocytes circulate in the peripheral blood of an adult human and are essential for efficient gas exchange and transport throughout the body. Erythrocytes have evolved a highly specialized physiology, shape and structure for this crucial role: in the course of their development, mammalian erythroid cells eliminate most of the major structures normally present in eukaryotic cells, including nuclei, mitochondria, Golgi and endoplasmic reticulum. These changes are a vital part of a developmental programme that improves efficiency of gas exchange, increases the flexibility of the erythrocyte allowing easier passage through narrow vessels and reduces the effort required of the heart to pump the cells around the body [1]. However, the losses, particularly of the nucleus, also prevent erythrocytes from responding to internal and external cues by altering gene transcription and mRNA abundance. Once the nucleus is lost at the orthochromatic erythroblast–reticulocyte transition, no more RNA is synthesized, and any further regulation of gene expression is necessarily post-transcriptional.

In humans, reticulocytes are shed from bone marrow into the bloodstream and then over the next 1–2 days they mature to erythrocytes, during which time haemoglobin content increases, but both translational capacity and RNA content declines. Mature erythrocytes can be easily distinguished from their immediate reticulocyte progenitors by supravital staining with reagents such as New Methylene Blue. Reticulocytes exhibit pronounced staining of the eponymous reticulin which is thought to be a lattice of translating ribosomes in the final throes of haemoglobin production. Mature erythrocytes do not bind the dyes, hence a lack of detectable RNA is a defining feature of the mature erythrocyte. Microphotometry of mature erythrocytes after Azure B staining indicated no RNA present in mature rabbit erythrocytes [2], and measurements of RNA content during in vitro maturation of Friend leukaemia virus-transformed murine reticulocytes to erythrocytes showed the amount apparently asymptotically approaching zero by the end of the maturation period [3]. However, although mature rabbit reticulocytes indeed have diminished numbers of ribosomes compared with immature stages, a significant number were still readily observed by EM (electron microscopy) [4], suggesting that some may be retained in the mature erythrocyte stage that immediately follows. Larger structures such as mitochondria are clearly absent from erythrocytes, but the loss of these during erythropoiesis seems to be mechanistically unrelated to the loss of RNA [5]. For example, inhibitors of autophagy which prevent mitochondrial elimination do not affect the loss of RNA from developing reticulocytes [6]. The cell-wide RNA-destruction programme is probably carried out by ribonucleases such as that described from rabbit reticulocytes, which is active on rRNA, tRNA and probably mRNA [7,8]. However, it is not known how many ribonucleases participate or how selective they are in their substrate choice. Neither is it known whether all RNAs are degraded at equal or different rates or to the same or different extents. The meagre literature on this subject suggests that RNA disposal during erythropoiesis has received little attention, even though adequate destruction of RNA is thought to be important for red cell function (to recycle adenine nucleosides for ATP replenishment [9]).

miRNA (microRNA) in erythrocytes

Given the widely held view that erythrocytes have no significant RNA content, it comes as something of a surprise to find that erythrocytes maintain plentiful amounts of miRNA [10,11]. Both studies identified abundant miRNA...
miRNAs are the best characterized class of several, novel, small (20–30 nt in length) RNAs that have been discovered within the last few years. Over 1000 different miRNAs are transcribed from the human genome and they exhibit widely varying patterns of expression and degrees of abundance. Their function is to regulate gene expression primarily by inhibiting the translation of mRNA [12,13], but translational promotion has also been reported [14]. Targeting the correct mRNA involves initial complementary Watson–Crick base-pairing between the mRNA and the miRNA. miRNAs accomplish this in partnership with a protein of the Argonaute family in an RNP (ribonucleoprotein) complex known as RISC (RNA-induced silencing complex) [15]. Thus the existence of miRNA in erythrocytes is surprising not only because of their presence, but also because the raison d’être of miRNA in other cells is to regulate gene expression through effects on mRNA translation, and this has long been thought to be absent from erythrocytes.

Other RNAs in erythrocytes

miRNAs are not, in fact, the first RNAs to have been found in erythrocytes. tRNA was reported to be present in mature erythrocytes [16], but the method by which reticulocytes were excluded as a possible alternative source of the RNA was not detailed. More convincingly, the small RNA polymerase III-transcribed transcripts Y1 and Y4 were shown to be present in mature erythrocytes [17]; density gradient depletion of reticulocytes from peripheral blood did not significantly diminish levels of these RNAs and neither were their levels altered much in blood samples exhibiting reticulocytosis. Therefore the authors concluded that significant amounts of the RNA must be present in mature erythrocytes. The absence of Y3 and Y5 RNA, which are normally present with Y1 and Y4 in nucleated cells, again illustrates how the loss of RNA during erythropoiesis is selective rather than wholesale and is more consistent with there being a reason for the maintenance of certain RNAs within erythrocytes than it being coincidence. Recent studies of Ro RNPs suggest that they function in the maintenance of integrity of other RNAs [18]. Therefore an obvious inference from the presence of Ro RNP in erythrocytes is that other RNAs exist in these cells whose integrity is important. The miRNAs described above are obvious candidates, but small amounts of rRNA and mRNA might benefit from protection and/or surveillance in the pro-oxidative environment of the erythrocyte.

Possible reasons for miRNA in erythrocytes

Chen et al. [10] showed that the miRNA pattern in human reticulocytes was very distinct from that in mature erythrocytes. Our own studies suggest the concentration of miRNA in erythrocytes is similar to that in nucleated cells and that the miRNAs are part of an active miRNP (miRNA-containing RNP) with Argonaute proteins (R. Lu and A.J. Hamilton, unpublished work). The selective retention of a distinct set of active miRNAs is more consistent with their having a function in erythrocytes than them being a random remnant of a general RNA-destruction programme. A direct role for the miRNA in the programmed destruction of RNA during erythropoiesis is unlikely because miRNA-directed cleavage of mRNA only occurs if near-perfect complementarity exists between miRNA and a mRNA [15] and very few human miRNAs have this property. Perhaps the most obvious explanation for the presence of miRNA in erythrocytes would be if these cells did, in fact, contain some translating mRNA upon which miRNPs could exert their acknowledged regulatory effects. However, this contradicts the well-established tenet that translation does not occur in these cells. There is good justification for the latter view. In countless routine clinical analyses on patient blood, erythrocytes fail to bind supravital dyes, a compelling testament to the drastic reduction in overall RNA content in these cells. It is also supported by studies of maturing reticulocytes showing a progressive reduction in RNA content to apparently zero levels [2,3,19]. As well as the evident reduction of RNA content, translational activity, as measured by uptake of radioactive amino acids, is close to zero in erythrocytes [20], and studies of reticulocytes show a decline in the ratio of polyribosomes to monosomes [4,21,22] with increasing maturity. However, the presence of miRNA, Y RNA and possibly tRNA show that the erythrocyte RNA content, although low, is not zero. It is possible then that the early studies might also have missed low levels of translation particularly if it were active only under certain conditions. Rikkind et al. [4], reporting an EM study of mat


\) is complete sufficient for \( \theta \). Consider \( T = X_{n:n}^2 \).

Obviously, \( E_\theta[T] = \frac{1}{4} \theta^2 (1 + 1/3n) = r(\theta) \). One should verify that \( E_\theta[T \mid X_{n:n}] = \frac{1}{4} (1 + \frac{1}{3n})(1 + \frac{2}{n})X_{n:n}^2 \). We leave it out as Exercise 7.5.21.

Again, if one first obtains the conditional pdf of \( T \) given \( X_{n:n} \) and evaluates \( E_\theta[T \mid X_{n:n}] \) directly, then one will realize what a clever approach the present one has been. ▲

### 7.6 Unbiased Estimation Under Incompleteness

Suppose that it we start with two statistics \( T \) and \( T' \), both estimating the same real valued parametric function \( r(\theta) \) unbiasedly. Then, we individually condition \( T \) and \( T' \) given the sufficient statistic \( U \) and come up with the refined Rao-Blackwellized estimators \( W = E_\theta[T \mid U] \) and \( W' = E_\theta[T' \mid U] \) respectively.

It is clear that (i) both \( W \) and \( W' \) would be unbiased estimators of \( r(\theta) \), (ii) \( W' \) will have a smaller variance than that of \( T \), and (iii) \( W' \) will have a smaller variance than that of \( T' \).

An important question to ask here is this: how will the two variances \( V_\theta(W) \) and \( V_\theta(W') \) stack up against each other?

If the statistic \( U \) happens to be complete, then the Lehmann-Scheffé Theorems will settle this question because \( W \) and \( W' \) will be identical estimators w.p.1. But if \( U \) is not complete, then it may be a different story. We highlight some possibilities by means of examples.

### 7.6.1 Does the Rao-Blackwell Theorem Lead to UMVUE?

Suppose that \( X_1, \ldots, X_n \) are iid \( N(\theta, \theta^2) \) having the unknown parameter \( \theta \in \Theta = (0, \infty), \chi = (-\infty, \infty), n \geq 2 \). Of course, \( \underline{U} = (\underline{X}, S^2) \) is sufficient for \( \theta \) but \( U \) is not complete since one can check that \( E_\theta[n(n+1)^{-1}\underline{X}^2 - S^2] = 0 \) for all \( \theta \in \Theta \) and yet \( n(n+1)^{-1}\underline{X}^2 - S^2 \) is not identically zero w.p.1. Now, let us work with \( T = \underline{X}, T' = a_n^{-1}S \) where \( a_n = \sqrt{2\Gamma(\frac{n}{2})}\Gamma(\frac{n+1}{2})/\sqrt{n-1} \) and the fact that \( (2.3.26) \) it follows that \( E_\theta[S] = a_n \theta \) and hence \( T' \) is unbiased for
\( \theta \) while obviously so is \( T \) itself. Now, \( \bar{X}, S^2 \) are independently distributed and hence we claim the following:

\[
E_{\theta}[\bar{X} \mid U] = \bar{X}, \quad E_{\theta}[S \mid U] = S.
\]

Thus, the Rao-Blackwellized versions of \( T \) and \( T' \) are respectively \( \bar{X}(= W) \) and \( a_n^{-1} S(= W') \). Clearly \( W \) and \( W' \) are both unbiased estimators for the unknown parameter \( \theta \). But observe that \( V_{\theta}(W) = n \theta^2 \) while \( V_{\theta}(W') = (a_n^{-2} - 1)\theta^2 \). Next, note that \( \Gamma(x + 1) = x\Gamma(x) \) for \( x > 0 \), \( \Gamma(\frac{1}{2}) = \sqrt{\pi} \) and evaluate \( V_{\theta}(W') \). Look at the Table 7.6.1.

( n )
( \theta^2 V_{\theta}(W) )
Exact ( \theta^2 V_{\theta}(W') )
Approx. ( \theta^2 V_{\theta}(W') )

2
.5000
((\pi/2) - 1)
.5708

3
.3333
((4/\pi) - 1)
.2732

4
.2500
((3\pi/8) - 1)
.1781

5
.2000
({32/(9\pi)} - 1)
.1318

Upon inspecting the entries in the Table 7.6.1, it becomes apparent that \( W \) is better than \( W' \) in the case \( n = 2 \). But when \( n = 3, 4, 5 \), we find that \( W' \) is better than \( W \).

For large \( n \), however, \( V_{\theta}(W') \) can be approximated. Using (1.6.24) to approximate the ratios of gamma functions, we obtain

\[
x^{b-a} \Gamma(x + a) \{\Gamma(x + b)\}^{-1} = 1 + \frac{1}{2}(a - b)(a + b - 1)x^{-1} + O(x^{-2}) \text{ as } x \to \infty. \tag{7.6.1}
\]

Now, we apply (7.6.1) with \( x = \frac{n}{2}, a = -\frac{1}{2} \) and \( b = 0 \) to write

\[
a_n^{-2} = \frac{1}{2}(n - 1)\frac{2}{n} \left\{1 + \frac{3}{4n} + O(n^{-2})\right\}^2
= (1 - \frac{1}{n}) \left\{1 + \frac{3}{2n} + O(n^{-2})\right\}
= 1 + \frac{1}{2n} + O(n^{-2}) \text{ as } n \to \infty. \tag{7.6.2}
\]

In other words, from (7.6.2) it follows that for large \( n \), we have

\[
V_{\theta}(W') = (a_n^{-2} - 1)\theta^2 \sim \frac{1}{2n} \theta^2. \tag{7.6.3}
\]

Using MAPLE, the computed values of \( \theta^2 V_{\theta}(W') \) came out to be \( 2.6653 \times 10^{-2}, 1.7387 \times 10^{-2}, 1.2902 \times 10^{-2}, 1.0256 \times 10^{-2}, 5.0632 \times 10^{-3} \) and \( 2.5157 \times 10^{-3} \) respectively when \( n = 20, 30, 40, 50, 100 \) and \( 200 \). The approximation given by (7.6.3) seems to work well for \( n \geq 40 \).
Khan (1968) considered this estimation problem but he first focussed on
the status of the MLE. Our goal is slightly different. Utilizing the two initial
unbiased estimators $T, T'$ we focussed on the Rao-Blackwellized versions and
compared their variances. This was not emphasized in Khan (1968). We find
that $W'$ can be better than $W$ even if $n$ is small ($\geq 3$) but for large $n$, the


 variance gets smaller as the SNR gets larger. Inserting (30) into (17) and (20), at high SNRs, we attain

$$P_{s_1} \approx \frac{13\xi K (N + K)}{48\rho N(K + 1)} \left( \frac{1}{\gamma_0} \right),$$

(31)

$$P_{s_2} \approx \frac{K}{N(K + 1)} \left[ K\omega + \frac{13\xi (N + K)}{48\rho} \right] \left( \frac{1}{\gamma_0} \right).$$

(32)

The corresponding coding gains are

$$c_1' = \frac{48\rho N(K + 1)}{13\xi K(N + K)},$$

(33)

$$c_2' = \frac{N(K + 1)}{K} \left[ K\omega + \frac{13\xi(N + K)}{48\rho} \right].$$

(34)

Particularly, as $K \to N$, (33) can reduce to the coding gain of the classical OFDM, as

$$c_0' = \frac{24\rho}{13\xi}.$$

(35)

Like the perfect CSI case, it can be seen from (31) and (32) that the MCIK-OFDM scheme under MMSE based $\epsilon^2$ achieve the diversity order of one. However, for high SNR, the attainable coding gains get smaller, i.e., $c_i' < c_i$ for $i = 0, 1, 2$. This degradation is caused by the impact of MMSE channel estimation error. Based on this, we provide the following theorem.

Theorem 3. Consider MCIK-OFDM systems. Denote by $\Delta_1$ and by $\Delta_2$ coding gain losses achieved by the ML and by the GD, respectively, under MMSE based uncertain CSI over the perfect CSI. Then, we have

$$\Delta_1 = 10 \log_{10} \left( \frac{N + K}{K} \right),$$

(36)

$$\Delta_2 = 10 \log_{10} \left[ \frac{K\omega + \frac{13\xi(N + K)}{48\rho}}{K\omega + \frac{13\xi K}{48\rho}} \right],$$

(37)

which satisfy $\Delta_1 > \Delta_2$.

Proof: Let the losses of coding gain be $\Delta_i = 10 \log_{10} (c_i/c_0')$ for $i = 1, 2$. Thus, utilizing (24) and (33) yields (36), while using (25) and (34) yields (37). Subtracting (37) from (36) leads to

$$\Delta_1 - \Delta_2 = 10 \log_{10} \left\{ 1 + \frac{NK\omega}{K\omega + \frac{13\xi(N + K)}{48\rho}} \right\} > 0.$$
This concludes the proof.

Remark 5. As shown in Theorem 3, the GD detector is less sensitive to the MMSE channel estimation error than the ML. This is because the loss of coding gain of the ML is larger than that of the GD.

Theorem 4. Denote by \( g' \) the coding gain that the MCIK-OFDM using the ML achieves over the classical OFDM, under MMSE CSI uncertainty. We have
\[
g' = 10 \log_{10} \left[ \frac{2N (K + 1)}{K (N + K)} \right] \text{ (dB)},
\]
and \( g' < g \), where \( g \) is given in (27).

Proof: Based on the definition of \( g' \), we have \( g' = 10 \log_{10} (c'_1/c'_0) \). Here, using \( c'_1, c'_0 \) given in (33) and (35), respectively, we obtain (38). Next, combining (27) and (38) leads to \( g - g' = 10 \log_{10} \left[ (N + K)/2K \right] > 0 \) for every \( K < N \), thus \( g' < g \). This concludes the proof.

Remark 6. Theorem 4 reveals that under MMSE CSI uncertainty, the coding gain achieved by MCIK-OFDM over the classical OFDM is smaller than that under the perfect CSI.

Finally, similar to Theorem 1 in the perfect CSI case, in this case, the SEP of the GD performs nearly the same as that of the ML as \( M \) increases, which can be shown from (31) and (32) with the steps used in Theorem 1.

V. NUMERICAL AND SIMULATION RESULTS

We now present numerical and simulation results to verify our theoretical analysis on the SEP of the MCIK-OFDM under various CSI conditions. For comparison, we show the average SEP for MCIK-OFDM schemes using the ML and the GD as well as the classical OFDM.

A. SEP of MCIK-OFDM under Perfect CSI

Fig. 1 shows the average SEP of MCIK-OFDM with \( N = 4, K = 2, M = 2 \), using both the ML and the GD. This figure also compares this MCIK-OFDM scheme with the classical OFDM at the same data rate of 1 bps/Hz. As seen from Fig. 1, both the theoretical and asymptotic curves are very tight to simulation results in a wide range of SNRs. This successfully verifies the accuracy of the derived expressions for the average SEPs of both the ML and GD. Moreover, the SEP of MCIK-OFDM and the classical OFDM achieve the same diversity order of one, under perfect CSI, as shown in Remark 1.

Fig. 2 illustrates the impact of the PSK modulation order \( M \) on the average IEP of MCIK-OFDM using the ML with \( N = 4, K = 2 \) and \( M = \{2, 4, 8, 16\} \). It is clear from Fig. 2 that the order \( M \) has a negligible impact on the IEP performance, which validates our analysis right after (16). We also see the tightness of the derived IEP, even at low SNRs.

Fig. 3 depicts the behaviour of the SEP of MCIK-OFDM using the ML and the GD at various \( K \). It can be seen that MCIK-OFDM with the ML and \( N = 4, M = 2 \) provides the difference of 6.5 dB SNR gain when increasing \( K \) from 1 to 3. However, greater \( K \) offers a higher data rate. In addition, Fig. 3 shows that compared to OFDM, the SNR gain of the \( K = 1 \) MCIK-OFDM with the ML achieves about 8 dB SNR gain for the SEP of \( 10^{-3} \). This validates Remark 3.
Fig. 4. Comparison between the average SEPs of the ML and the GD, with the MCIK-OFDM of $N = 2$, $K = 1$ and $M = \{2, 8, 16\}$.

Fig. 5. Impact of fixed $\epsilon^2$ on the average SEPs of different MCIK-OFDM schemes using both the ML and GD detectors, under different values of $\epsilon^2$. It is shown from Fig. 5 that the average SEPs suffer from error floors as the SNR increases. These error floors get higher when increasing $\epsilon^2$. More interestingly, as $\epsilon^2 = 0.1$, the GD outperforms the ML in terms of the SEP, especially at high SNRs. This observation validates the accuracy of Theorem 2 and Remark 4. As $\epsilon^2$ decreases, the SEP gap between the two detectors becomes smaller.

C. SEP of MCIK-OFDM under MMSE CSI Uncertainty

Fig. 6 demonstrates the effect of the MMSE imperfection on the SEP of MCIK-OFDM using the ML and GD, when $N = 4$, $K = 2$ and $M = 2$. As seen from Fig. 6, under MMSE CSI uncertainty, MCIK-OFDM using the ML suffers from a considerable loss of nearly 5 dB SNR gain compared to the perfect CSI case. The loss raised by the GD is much smaller, being around 0.5 dB. Thus, the GD is less sensitive to MMSE CSI uncertainty than the ML.

In Fig. 7, we depict the average SEP of the MCIK-OFDM using the ML with $N = 4$, $K = 3$, $M = 4$ under MMSE imper


>

Y = Young; M = Masters; T = Trained; U = Untrained; MVC = Maximal Voluntary Contraction; VT1 = Ventilatory Threshold 1; VT2 = Ventilatory Threshold 2; 10ST = 10 second sprint; CK = Creatine Kinase; LDH = Lactate Dehydrogenase; Pt = Peak Twitch; Ct = Contraction Time; HRt = Half Relaxation Time; RMS = Root Mean Square; CMJ = Counter Movement Jump; HR = Heart Rate; DE = Delta Efficiency<|endoftext|>Age-related changes in performance and recovery kinetics in masters athletes: A narrative review

Borges, Nattai; Reaburn, Peter; Driller, Matthew; Argus, Christos

Published in:
Journal of Aging and Physical Activity

DOI:
10.1123/japa.2015-0021

Licence:
CC BY-NC-ND

Link to output in Bond University research repository.

Recommended citation(APA):
Age-related Changes in Performance and Recovery Kinetics in Masters Athletes

Submission Type: Literature Review

Nattai Borges¹
Peter Reaburn¹
Matthew Driller²
Christos Argus³, ⁴

¹ School of Medical and Applied Sciences, Central Queensland University, Rockhampton, Australia
² Department of Sport and Leisure Studies, The University of Waikato, Hamilton, New Zealand
³ Research Institute for Sport and Exercise, University of Canberra, Canberra, Australia
⁴ ACT Brumbies Rugby, Canberra, Australia

Corresponding Author

Mr Nattai Borges
School of Medical and Applied Sciences
Central Queensland University
Bruce Highway
Rockhampton, Queensland, 4702
Australia
Phone: +61 7 4930 9720
Email: n.borges@cqu.edu.au

Abstract Word Count: 227
Number of References: 95
Text-Only Word Count: 4881
Number of Figures and Tables: 3
Age-related Changes in Performance and Recovery Kinetics in Masters Athletes:

A Narrative Review

Submission Type: Literature Review
Abstract

Despite increasing participation rates in masters sport and extensive research examining age-related changes in performance, little is known about the effect of age on recovery kinetics in masters athletes. This narrative review focuses on the relationship between ageing and sports participation, and their effect on both performance and recovery following an exercise bout. Current research suggests the effect of age on performance and recovery may be smaller than originally suggested and that increasing sedentary lifestyles appear play a larger role in any observed decrements in performance and recovery in masters athletes. Currently, it appears that performance decrements are inevitable with age. However, performance capacities can be maintained through systematic physical training. Moreover, the limited current research suggests there may be an age effect on recovery kinetics following an exercise bout although further research is required to understand the acute and chronic recovery processes in the masters athlete.
Masters athletes are defined as individuals who systematically train and compete in organised forms of

TO DATE, THERE IS LIMITED RESEARCH (EASTHOPE ET AL., 2010; SULTANA ET AL., 2012) AND ANECDOTAL EVIDENCE TO SUGGEST THAT AS ATHLETES AGE THEY MAY EXHIBIT IMPAIRED RECOVERY KINETICS (TIME TAKEN TO RECOVER FROM A GIVEN EXERCISE BOUT) COMPARED TO YOUNGER ATHLETES. CONSEQUENTLY, AGE-RELATED REDUCTIONS IN RECOVERY KINETICS MAY HAVE AN EFFECT ON SUBSEQUENT BOUTS OF EXERCISE TRAINING, LEADING TO A REDUCTION IN OVERALL TRAINING LOAD AND A POTENTIALLY INCREASED
risk of injury. A previous review (Fell & Williams, 2008) has examined the effect of age on skeletal muscle
recovery after exercise although due to the paucity of research into masters athletes at the time, the review relies
on a tentative link between animal studies and investigations comparing young and non-athletic older populations
to draw conclusions about a possible age effect on recovery. Recent research comparing younger and masters
athletes has increased knowledge in this specific population and shown the significance of neuromuscular
recovery in masters athletes. Despite this, limited research has empirically examined recovery kinetics of older
versus younger athletes (Bieuzen, Hausswirth, Louis, & Brisswalter, 2010; Darr et al., 1988; Easthope et al., 2010;
Fell, Haseler, Gaffney, Reaburn, & Harrison, 2006; Fell, Reaburn, & Harrison, 2008). Moreover, the possible
mechanisms explaining the slower recovery kinetics in older athletes remain to be investigated. This narrative
review will examine the effects that physical activity and systematic training may have on performance and
recovery in both sedentary and athletic ageing populations and highlight the need for further research into recovery
within masters athletes.

2 Methods

A literature search was conducted between April 2013 – January 2015 on the PubMed, Scopus and SPORTDiscus
databases. Search terms included “Age” OR “Masters” OR “Older” OR “Veteran” AND “Exercise” OR
“Performance” OR “Fatigue” OR “Recovery”. All languages and articles types were included in the search to
increase the number of articles. The reference lists of the resultant articles were examined for further articles not
found during the literature search. Articles comparing younger and masters athletes that failed to match their
subjects for training load were excluded. No other exclusion criteria were applied.

3 The Effects of Physical Activity and the Ageing Process on Physical Performance

The ageing process leads to a number of physical changes in both a normal ageing and masters athlete populations
that can affect aerobic and anaerobic performance (Brisswalter, Wu, Sultana, Bernard, & Abbiss, 2014; Reaburn
& Dascombe, 2009; Tanaka & Seals, 2008) as well as muscular strength and power performance (Burd et al.,
2013; Korhonen et al., 2012; Louis et al., 2012; Peiffer et al., 2010b).

Sedentary Ageing Population and Physical Performance

Both maximal oxygen uptake and maximal heart rate have been shown to be reduced in a normal ageing
population (Carrick-Ranson et al., 2013; Sabapathy, Schneider, Comadira, Johnston, & Morris, 2004). Similarly,
muscular strength and power have also been shown to decline in ageing sedentary populations (Cruz-Jentoft et al.,
An investigation of 301 sedentary healthy Australian males and females demonstrated that younger participants were significantly stronger as measured by one-repetition maximum strength tests (chest press, seated row, leg extension and leg press) and performed significantly better in functional performance tests such as a 400m walk, 6m walk, 6m backwards walk and sit to stands than individuals over 65 years of age (Peiffer et al., 2010b). These decreases in strength and functional abilities have been suggested to be linked with a decreasing muscle cross-sectional area specifically in type II muscle fibres in older sedentary individuals (Gouzi et al., 2013).

High intensity training such as resistance training into older age has also been shown to enhance muscular strength and power performance (Aagaard, Suetty, Caserotti, Magnusson, & Kjaer, 2010; Latham, Bennett, Stretton, & Anderson, 2004; Steib et al., 2010). An investigation by Deley et al. (2007) demonstrated similar significant improvements in physical parameters in elderly (>70 years) sedentary subjects following one year of moderate intensity training. The researchers reported that training for one hour three times a week with a combination of aerobic, strength, and flexibility exercises, plus adapted Tai-chi, lead to significant improvements in maximal oxygen uptake (14.8%), distance walked in six minutes (10%), and maximal muscle strength of the knee extensors (15.2%) and plantar flexors (17.4%) in the intervention group compared to an age-matched control group who maintained normal activity levels. Therefore, in a normal ageing population the research suggests that physical performance decreases with age although improvements can be made through systematic physical training.

The Masters Athlete and Physical Performance

Similar trends are reported in masters athletes as declines in both maximal oxygen consumption and maximal heart rate have been observed in masters athletes from a range of sports (Gent & Norton, 2013; Kusy & Zielinski, 2014). Peak endurance performance has been shown to be maintained until approximately the age of 35 years after which it declines slowly until the age of 50-60 years after which there is an increased rate of decline due primarily to a decrease in maximal oxygen consumption (Pimentel, Gentile, Tanaka, Seals, & Gates, 2003; Ransdell, Vener, & Huberty, 2009; Tanaka & Seals, 2008). Decreases in the strength and power have also been observed in an ageing athletic population by Korhonen et al. (2006) who reported that both type II muscle fibre size and


3
cfbd_key (register_cfbdb), 95
cfbd_metrics, 28
cfbd_metrics_ppa_games, 29
cfbd_metrics_ppa_games(), 29
cfbd_metrics_ppa_players_games, 30
cfbd_metrics_ppa_players_games(), 31
cfbd_metrics_ppa_players_season, 32
cfbd_metrics_ppa_players_season(), 33
cfbd_metrics_ppa_predicted, 34
cfbd_metrics_ppa_predicted(), 34
cfbd_metrics_ppa_teams, 34
cfbd_metrics_ppa_teams(), 35
cfbd_metrics_wp, 36
cfbd_metrics_wp(), 36
cfbd_metrics_wp_pregame, 37
cfbd_metrics_wp_pregame(), 38
cfbd_pbp_data, 38
cfbd_play, 49
cfbd_play_stats_player, 57
cfbd_play_stats_player(), 57
cfbd_play_stats_types, 59
cfbd_play_stats_types(), 57, 59
cfbd_play_type_df, 39, 55
cfbd_play_type_df (data), 91
cfbd_play_types, 60
cfbd_play_types(), 60
cfbd_player (cfbd_players), 50
cfbd_player_info, 50
cfbd_player_info(), 31, 32, 51, 53, 57
cfbd_player_returning, 52
cfbd_player_returning(), 52
cfbd_player_usage, 53
cfbd_player_usage(), 54
cfbd_players, 50
cfbd_plays, 54
cfbd_plays(), 55
cfbd_rankings, 60
cfbd_rankings(), 61
cfbd_ratings, 61
cfbd_ratings_elo, 62
cfbd_ratings_elo(), 63
cfbd_ratings_sp, 63
cfbd_ratings_sp(), 63
cfbd_ratings_sp_conference, 65
cfbd_ratings_sp_conference(), 65
cfbd_ratings_srs, 66
cfbd_ratings_srs(), 67
cfbd_recruiting, 67
cfbd_recruiting_player, 68
cfbd_recruiting_player(), 68, 69
cfbd_recruiting_position, 70
cfbd_recruiting_position(), 68, 71
cfbd_recruiting_team, 71
cfbd_recruiting_team(), 71
cfbd_stats, 72
cfbd_stats_categories, 73
cfbd_stats_categories(), 73
cfbd_stats_game_advanced, 73
cfbd_stats_game_advanced(), 74
cfbd_stats_season_advanced, 76
cfbd_stats_season_advanced(), 76
cfbd_stats_season_player, 79
cfbd_stats_season_player(), 80
cfbd_stats_season_team, 82
cfbd_stats_season_team(), 82
cfbd_team_info, 85
cfbd_team_info(), 9, 85
cfbd_team_matchup, 86, 87
INDEX

cfbd_team_matchup_records, 87
cfbd_team_matchup_records(), 88
cfbd_team_roster, 88
cfbd_team_roster(), 88
cfbd_team_talent, 89
cfbd_team_talent(), 89
cfbd_teams, 84
cfbd_venues, 90
coaches (cfbd_coaches), 6
conferences (cfbd_conferences), 7
data, 91
database (update_cfb_db), 96
DBI::dbConnect(), 96
draft (cfbd_draft), 8
drives (cfbd_drives), 11
espn_cfb_pbp, 92
espn_cfb_scoreboard, 92
espn_cfb_scoreboard(), 92
espn_metrics, 93
espn_metrics_wp (espn_metrics), 93
espn_metrics_wp(), 93
espn_ratings, 94
espn_ratings_fpi (espn_ratings), 94
has_cfb_key (register_cfb), 95
load_cfb_pbp, 95
nfl (cfbd_draft), 8
nfl_draft (cfbd_draft), 8
nfl_teams (cfbd_draft), 8

pbp_data (cfbd_pbp_data), 38
play-by-play (cfbd_pbp_data), 38

qs::qdeserialize(), 95

recruiting (cfbd_recruiting), 67
register_cfb, 95

update_cfb_db, 96
update_cfb_db(), 95<|endoftext|>McCarthy Creek

Access: Trail begins in downtown McCarthy, just past the historic hardware store.

Distance: 5 miles one-way, 10 miles round-trip

Time: 4-6 hours round-trip

Maps: Trails Illustrated map of Wrangell-St. Elias, USGS McCarthy 1:63,360 (B6)

Difficulty: Moderate

Highlights: Scenery, solitude, easy access

Route: To access McCarthy Creek, walk through town on the main road, past the historic hardware store. When the road ends, turn left onto a short trail to the river. Cross McCarthy Creek via a small footbridge. Climb up the bank to a gravel road. The trail starts at the end of the first steep switchback (approximately 200 yards from the footbridge). Trail leads through the McCarthy Creek creekbed. After about three miles the river has washed out the route. Walk up and over the slump paralleling the creek to avoid crossing the river. The trail ends at the river, between an old cabin and the area where the original route crossed the river.

At this point, you will need to cross the river or turn around. Warning: McCarthy Creek is actually a fairly large river. It is possible to cross at low water but may be treacherous at higher water volumes. Use your best judgment and turn around here if the river looks dangerous. If you chose to cross the river, continue about 300 yards where you will cross back. Shortly thereafter, a trail leads you through an original tunnel left from the mining era. Return via the same route.

Hazards: Floods frequently wash out portions of this route. Use your best judgment regarding safety and current conditions. Creek crossing can be very hazardous at high water volumes. Be prepared to turn back early if necessary.

Notes: If continuing into the upper reaches of the McCarthy Creek drainage, please be aware that private property exists. Please respect private property by not trespassing. Hikers planning multiple-day backpacking trips in this area should seek additional information regarding private property locations.
The trail starts at the end of the first steep switchback (approximately 200 yards from the footbridge).<|endoftext|>From 2006-2013 spring yearling salmon at about 8 inches were stocked each May in lakes Waywayanda and Aeroflex immediately upon their arrival from Massachusetts. Salmon at this size usually feed on insects and macroinvertebrates; by the end of their first summer their food preference will shift to fish (alewives).

In 2013 some of the spring yearlings received in May were retained in the Hackettstown State Fish Hatchery and grown to a larger size. A portion of these fish were later stocked in lakes Waywayanda and Aeroflex in late fall, at an average size of 14 inches. Some fish remained in the hatchery over the winter and were stocked in Tilcon Lake in Morris County in April of 2014. These fish averaged 18 inches.

The landlocked salmon populations are maintained at these three lakes through annual stockings. While mature salmon may migrate to inlets and outlets and attempt to spawn, it is unlikely that natural reproduction would produce enough fish to maintain the fishery. The stocking rate and harvest regulations are intended to provide anglers with an opportunity to catch salmon that range from 12-17 inches and an occasional salmon in excess of 17 inches, weighing 3 pounds or more.

Landlocked salmon are closely related to brown trout (*Salmo trutta*), and anglers may have difficulty telling them apart. Because size and creel limits are different for salmon and trout, anglers need to know the difference in order to comply with the regulations and quickly release salmon smaller than 12 inches. When in doubt about identifying salmon and brown trout, play it safe and release the fish unharmed!<|endoftext|>Football Money League
Changing of the guard
Contents

Introduction 4
by Dan Jones

The Deloitte Football Money League 6

Leagues within the Money League? 22
by Rich Parkes

The Real deal 25
by Austin Houlihan
Welcome to the 2006 Deloitte Football Money League. This is the ninth year of the publication, profiling the largest clubs in the world’s most popular sport for the 2004/05 season. A number of methods may be used to determine the size of a club – including measures of fanbase, attendances, TV audiences, or on pitch success. However, for the purposes of this publication, we look at the best publicly


 by any user on the materials contained on this website.

For the latest updates and more information, visit www.betterhealth.vic.gov.au<|endoftext|>All hunters who harvest a white-tailed deer or wild turkey are required to complete the game check process.

**FILL IN THE PERMIT**

- Fill in the deer or wild turkey permit upon harvest with the date, time, and county of kill.
- Exempt landowners are required to make a tag and include their name, date, time, and county of kill.

Once the hunter leaves the game unattended, the completed permit or tag, or confirmation code, must be attached. The permit or confirmation code is required to remain with the game at all times.

**COMPLETE GAME CHECK**

Hunters may check game and receive a confirmation code in one of these ways:

- Call 1-877-TAG-IT-OH (1-877-824-4864).
- Exempt landowners call 1-866-703-1928 for operator-assisted landowner game check. Fees apply.
- Visit ohiogamecheck.com, then select COMPLETE GAME CHECK.
- Visit any authorized license sales agent. A list of sales agents may be found at wildohio.gov. Be sure to bring the permit number to the license agent.

The confirmation code must remain attached to the game and its parts.<|endoftext|>Therapeutic Use Exemptions and the Doctrine of Double Effect

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oro.open.ac.uk
THERAPEUTIC USE EXEMPTIONS AND THE DOCTRINE OF DOUBLE EFFECT

Without taking a position on the overall justification of anti-doping regulations, I analyse the possible justification of Therapeutic Use Exemptions (TUEs) from such rules. TUEs are a creative way to prevent the unfair exclusion of athletes with a chronic condition, and they have the potential to be the least bad option. But they cannot be competitively neutral. Their justification must rest, instead, on the relevance of intentions to permissibility. I illustrate this by means of a set of thought experiments in which only an athlete’s intentions vary. I argue that the Doctrine of Double Effect sheds some light on TUEs and illustrate this by applying different readings of the DDE to the thought experiment. This underpins a justification of anti-doping exemptions very different from than the approach adopted by the World Anti-Doping Agency (WADA). I argue for three changes to bring TUEs in line with this understanding: rewriting of the regulations, transparency, and a greater role for athletes in determining what exemptions are allowed, and when.

Keywords Therapeutic Use Exemptions, Doctrine of Double Effect, Doping, Anti-Doping, Intentions, Strict Liability, PEDs
In September 2016 the Russian sports hackers Fancy Bears released the confidential hacked files of Bradley Wiggins and Chris Froome, both British winners of the Tour de France. The records showed that Wiggins and Froome had both raced under Therapeutic Use Exemptions (hereafter TUEs) which had allowed them to use drugs on the proscribed list maintained by the World Anti-Doping Agency (WADA). Wiggins, in particular, had gained a TUE for using corticosteroids on three different occasions to treat asthma related conditions. Reactions in the British press, both national and the cycling press varied. Some argued that Wiggins had sailed close to the wind and that he had abused the TUE regulations. Others suggested that he had acted within the rules, and had done nothing wrong. Team Sky, and Wiggins himself, made both of these latter claims. Bradley Wiggins was interviewed on the Andrew Marr show on 29th September 2016 about the corticosteroids:

Marr: Now, the trouble with this particular drug is that lots of people say it is also a performance enhancer. David Millar said it was the most potent drug that he’s ever taken.

Wiggins: Yeah, but... I think... they were abusing that drug, and this was to cure a medical condition. (2016)

The set of anti-doping regulations and practices adopted by WADA has included a set of provisions for TUEs since 2005. The origins of TUEs are found in the work of the International Olympic Committee (IOC) medical committee in the late 1980s and early 90s. TUEs allow the use of substances and methods that would otherwise be prohibited because of their performance-enhancing effects. In this paper I examine some possible justifications of such exemptions. In doing so, I will pick through some of the guidelines in order to attempt a rational reconstruction (Habermas 1979) of the arguments, since no carefully worked out moral analysis has been published.

I will argue that the justification of exemptions based on therapeutic use is, with some caveats, a matter of intentions. And this is important because the rhetoric surrounding anti-doping regulation in general reflects an exclusion of intentions, and a central role for the principle of strict liability (McNamee and Tarasti 2010). I argue that, in this area, this is a mistake. If we view TUEs in a different light, justified primarily by intentions, then certain conclusions follow about their regulation

The Problem

TUEs are a special case of a growing phenomenon in public policy: a ‘rule and exemption’ approach (Barry 2001). On this approach, a rule is applied, but an exemption is available for a set of special cases. We must ask what it is about these supposed special cases that makes them morally distinctive. A simple answer is that the general rule, universally applied, seem to give the wrong result. Take, for example, the UK law requiring motor cyclist to wear helmets which was introduced in 1971 and revised in 1976 by the introduction of an exemption for Sikhs. Whether or not this exemption is justified, it is the reason given - religious observance - that must do the justificatory work.

There are striking similarities between some of the arguments around TUEs and arguments about cultural exemptions. For example, at an early stage of the controversy in the 1970s that led to an exemption for Sikhs, Lord Widgery ruled against an exemption:

No-one is required to ride a motor cycle. All that the law requires is that if you do ride a motor cycle you must wear a crash helmet. (Poulter 1988, 293)
Sikhs were not required to ride motorbikes, so the exemption did not hold, or, at least, so ruled Widgery. Equally, it might be argued, no-one is required to take part in elite sport. But if you do, you must not take banned substances.

The case for a rule and exemption approach must sit between two positions: on one hand the case for uniformity must be strong otherwise the solution ought to be to remove the rule. On the other hand, it must not be too strong, otherwise there is no case for exemptions. Everything that counts for the strictness of the ban on PEDs counts against the provision of exemptions. How can this middle way be justified? In order to answer this question, we need to look at a regulatory world without TUEs.

In the absence of TUEs, an athlete with a chronic condition treatable only with a banned substance faces an invidious choice. They can take the substance and abandon elite sport. Or they can decide not to use the banned substance and suffer health and competitive loss. In the long term they are likely to abandon elite sport because the competitive loss is likely to be unsustainable.

How bad are these two options? Quite bad. Athletic identity is performative so making performance impossible undermines identity. Competition may be the athlete’s livelihood. Depriving an athlete of their identity and livelihood is a very high price for something that is not the athlete’s fault. It looks as if this is unfair, on a standard pre-theoretic understanding of fairness that involves getting what we deserve.

One response to such concerns is merely to shrug one’s shoulders and opine that life is tough. Here is the ruling of the Court for Arbitration in Sport (CAS) in Quigley v UIT in a related context; a case of the accidental absorption of a prohibited substance:

...it is also in some sense unfair for an athlete to get food poisoning on the eve of an important competition. Yet in neither case will the rules of the competition be altered to undo the unfairness. Just as the competition will not be postponed to await the athlete’s recovery, so the prohibition of a banned substance will not be lifted in recognition of its accidental absorption. The vicissitudes of competition, like those of life, generally may create many types of unfairness whether by accident or the negligence of unaccountable persons which the law cannot repair. (1995, 6)

There is sleight of hand at work here. What the law can and cannot repair, is precisely what is at issue. Sports regulations may partly reflect underlying natural facts about the world, but they are also in part, constructions, and they can be constructed in different ways. The analogy made in the Quigley case suggests three cases: an


 as our spray program for pre-emergence control, we use Barricade everywhere in the irrigated areas where we do not want tracked-off volunteer rye seed to germinate and this also controls a variety of weeds in our irrigated areas. We try to apply other pre-emergent applications well ahead of any forecast rain event in non-irrigated areas. For post-emergent control we use Manor, Kerb, Princep and others. Once our overseeded grasses are up and established we try to topdress once every three-four weeks or as needed.
Super Tips by Darren Davis

Keep Your Employees; Pay Attention to Detail

Recently I spent a few hours with my colleague Tim Hiers, golf course manager at The Old Collier Golf Club in Naples. With Tim's tenure in the profession, he has witnessed many innovations, seen countless trends in the business and is a very valuable source of information. Taking advantage of his knowledge, I challenged Tim with this question, "If you could offer only one piece of advice to a fellow Golf Course Superintendent, and he had no prior knowledge of the individual's operation or their duration in the industry, what secret to success would he offer?"

After a brief pause he responded, "Always treat people well, but even more importantly clean up your facility; a clean, organized facility will give outsiders the impression that you truly care about the investment that you are maintaining and the safety of your biggest asset, your employees."

That piece of advice is the focus of this "Super Tip".

Employee Morale

Flags from around the world, representing the employee's country of origin, hang from the ceiling (Photo 1). The flags are an employee morale technique that Tim has employed to provide staff members a connection to their homeland. Tim admits that the idea is one that he had seen at other golf course facilities and he thought it was worth replicating. While some of the employees may only be temporary residents of the United States, Tim feels as long as they are in our country and employed at Old Collier, he wants these individuals to feel that they are part of an "extended family" or the "team at Old Collier". Tim added, "It is also a way to bring home into work and create a conversation piece among employees." This was also the motivation for mounting several large scale maps on the wall of the equipment storage area where he has labeled the "home" of each employee (Photo 2).

Pegboard

In the equipment repair area at Old Collier, peg board has been affixed to the walls (Photo 3). The first impact that the peg board had on my impression in the area was aesthetics. The area took on an organized "warehouse type" look, which is atypical of what I have seen at many other golf course facilities. The pegboard was also functional as hooks can be installed to hang and organize tools and other items. A third benefit is that the pegboard serves as a good sound absorber by buffering noise echoed from the building's metal walls and concrete floors.

Equipment Storage

In the equipment storage area, after each piece of equipment has been cleaned and put away for the night, all of the seats, beds and cowlings are raised to increase drying potential (Photo 4). Tim commented, "It is common sense that when you combine moisture and metal for an extended period of time rust becomes an issue." Ceiling fans are connected to a timer switch that turns the fans on from 6 pm to 10 pm each night to improve the drying process to protect the equipment.

Photo 1. Old Colliers displays flags of the countries represented by staff members.

Photo 2. World Maps with pins representing employees also show the states and countries the staff hail from.

Photo 3. Pegboard wall covering in the shop helps deaden sound and keep items neatly organized and stored.

Photo 4. Opening up beds and cowlings helps equipment to dry quickly and completely to help prevent corrosion.
end. This is because our bermudagrass does not come out of the cool weather very well primarily due to our nematode populations and shade. We keep the overseeding as long as possible without impeding the growth of the bermudagrass. We do lower the height of cut gradually, and brush, verti-groom and vertical mow, but we have never used any herbicides to take out our overseeding. We also do a lot of hand watering of the hot spots to prevent premature thinning before the bermudagrass is actively growing.

Buddy Keene

Southwest Florida
Weather is the Wild Card in Game Of Overseeding

"It was the coldest, wettest, busiest winter with the quickest spring warm up we've ever had."
- Stuart Taylor, GCS

Transition woes this spring had Stuart Taylor of the Riverwood GC in Port Charlotte scratching his head in disbelief. Says Taylor, "We used the same cultural practices we have used successfully the past five years and we used the same Poa trivialis (75 percent) and bentgrass (25 percent) blend that we used and liked last year."

So what was the difference?
"There was an immense difference in the weather this year. We have been averaging 10 frosts a year the last few years. This year we had 30 frosts. The winter was wetter."

Riverwood
Overseeding Practices

Preparation
- Verticut greens 3 ways.
- Verticut tees and fairways 2 ways
- Scalp roughs

Seeding Rates
- Greens 8 lbs/M Poa trivialis/bentgrass blend (75%/25%)
- Tees 400 lbs/A; Fairways 320 lbs/A; Roughs 210 lbs/A

We had 25 inches more rainfall than normal, and we had more traffic than ever as we experienced our busiest winter season ever with around 240 rounds a day. It didn't get much better going into spring. We had frost on April 1st and seven days later it was 85 degrees. The grass didn't know whether to come or go. It was very difficult to manage since the conditions were so atypical and changeable"

The transition frustration for Taylor was magnified by the fact that he felt like he had a great overseeding establishment. "Everything looked great in the fall. The seed went down smoothly, germinated and grew in. For nine months beginning in September, we had the best greens we've ever had, and then for 30 days beginning in May we've had the worst greens in five years. They are coming around now."

"We are on the frost line on the west coast. Thirty miles south and maybe overseeding could be optional, but we are also a development course so aesthetics are a critical issue year round for real estate sales and member satisfaction. So, overseeding is not optional. The trade-off is the members are kept informed and we brought in the USGA to also help explain transition problems."

"Some of our worst areas were on..."
HANDS ON

greens that came back with the best soil tests. Some of the thin areas were problematic since they were on shady greens to begin with. Others thin spots tended to occur in hydrophobic areas. To address this we are going to aerify with 3/4" hollow tines and topdress with a sand and Profile mix for more uniform moisture control along with a program of using Cascade and other wetting agent materials."

Stuart Taylor

Central-Northeast

Programs Haven't Responded to Milder Winters

"This year reminded me of the winters of the 70s and 80s.
- Butch Singo, Harrell’s, Inc.

Butch Singo is a sales representative for the Harrell’s Fertilizer Company, and his territory runs from Kissimmee to Jacksonville. I asked Butch his take on this year's overseeding challenges.

"Overseeding programs have not changed much in my territory in response to the mild winters," he said. "As usual, some courses experienced rougher transitions than others. Most of my customers know that the weather can be unpredictable and cause havoc to playing conditions in the winter without the insurance of overseeding."

"Successful establishment was very weather dependent as usual. Those who tended to go early in the fall had better luck than those who were scheduled later and got caught when the rainy weather hit and washed a lot of seed away. Mild weather early belied the density of the overseeding and when the severe cold weather hit and the bermudagrass went dormant, people found out much or how little seed they really had established."

This year really reminded me of the winters I experienced as a superintendent in the 70s and 80s when we would typically have 20-30 frosts a year. A lot of superintendents and golfers haven’t seen those kinds of winters in a long time and golfers often have short memories. Now since the second week in May, we’ve had high temperatures and low humidity, causing the overseeding to check out too quickly and everyone is scrambling to push the bermudagrass to fill in as quickly as possible."

Butch Singo

West-Northwest

Down Time is Nice; Preparation is Real Key To Success

"Preparation is the key to success.
- John Cunningham, GCS

Butch Singo is a sales representative for the Harrell’s Fertilizer Company, and his territory runs from Kissimmee to Jacksonville. I asked Butch his take on this year's overseeding challenges.

"Overseeding programs have not changed much in my territory in response to the mild winters," he said. "As usual, some courses experienced rougher transitions than others. Most of my customers know that the weather can be unpredictable and cause havoc to playing conditions in the winter without the insurance of overseeding."

"Successful establishment was very weather dependent as usual