Letter from W[illia]m G. Kerckhoff to W[illia]m H. Knight, 1899 Apr 28.

[ COPY ]WM.G. KERCKHOFF,T. P. LUKENS, CHARLES SILENT.JOHN F. FRANCIS,M. L. GRAFF,ADOLPH PETSCH,ABBOT KINNEY.Forest and water Assoriationof Lus Angeles county.[Los Angeles Branch of the Forest and Water Society of Southern California.]WM.G.KERCKHOFF. president,254 S. Los Angeles St.,T.P.LUKENS, Vice-pres.,pasadena.WM.H.KNIGHT, Secretary,27Bryson block.Lus Angeles, Cal. April 28, 1899.To the HonorableSECRETARY OF THE INTERIOR,Washington, D. C.Dear Sir:The Forest and Water Association of Los Angeles County desires most respectfully to call your attention to the following facts: The conservation of our mountain forests is a work of the most vital importance to the people of Southern California. In noother locality of the United States is the welfare of its people so dependent on the protection of its forests, and the preservation of its water sheds.During the past three years a very large proportion of our forest reservations has been devastated and denuded by forest fires and the herding of sheep and other stock upon them, and the damage and loss to Southern California from these causes has been incalculable.We are now approaching the dry season of another year, in a succession of years with a very limited rainfall, and as yet with nosteps taken, so far as we have learned, to provide a force of men at all adequate to properly care for these reservations during the coming dry season; and it is imperative that some suitable action be taken at once in the line of caring for these reservations in a manner commensurate with the great importance of the work.We would, most respectfully yet most urgently, request that you grant us, at the earliest possible time, adequate aid for properly caring for these reservations, and would suggest:1. That the herding of sheep or other stock upon the reservations, or the passage of stock over them, (which is often used as a pretense in order to get an opportunity to use them for pasture) be absolutely prohibited.2. Large portions of the Sierra Madre Range are very rugged and precipitous, being almost inaccessible except by the use of trails, the construction of which should be provided for so that fires may be readily combatted.,br\u3e3. The forest reservations are largely used for the purpose of camping in the summer time, and many of the forest fires are to tributable to the06195 Forest and \u27water Assariation. No. 2.careless use of camp fires. We recommend a system of permits to be granted at the entrances to these reserves, under such regulations as will not make it a hardship upon the people desiring to camp, but which at the same time will keep out irresponsible parties and check the careless use of fire.4. In addition to the force required in other forest reservations of Southern California, we estimate that the San Gabriel Reservation, which is mainly within this County, will require at least two companies of soldiers.5. When civilians are selected for patrolmen, we suggest that they be taken from the mountaineers who are familiar with these localities.6. We also urge the importance of replanting the denuded portions of our mountains as rapidly as possible to such varieties of trees as are known to be best adapted to the conditions and requirements. If permitted to remain bare for any length of time, the rain will gully the steep slopes and wash away the little remaining soil, carrying debris to cover the rich valley lands, and there will be no water for irrigation.A Forestry School has been organized under the auspices of the University of Southern California for the purpose of furnishing educated foresters to the Government. Associations, general and local, for the protection of our forest reservations, are being organized all over Southern California. These embrace our most prominent citizens who are giving it much careful thought and attention, and who are desirous of aiding and upholding the Government in every way possible. We believe that these organizations, if permitted, could furnish the Department with many valuable suggestions. In this connection we tender to the Government the aid and assistance of our Association.Very respectfully,WM. G. KERCKHOFF, President.WM. H. KNIGHTSecretary

A new invariant on hyperbolic Dehn surgery space

In this paper we define a new invariant of the incomplete hyperbolic structures on a 1-cusped finite volume hyperbolic 3-manifold M, called the ortholength invariant. We show that away from a (possibly empty) subvariety of excluded values this invariant both locally parameterises equivalence classes of hyperbolic structures and is a complete invariant of the Dehn fillings of M which admit a hyperbolic structure. We also give an explicit formula for the ortholength invariant in terms of the traces of the holonomies of certain loops in M. Conjecturally this new invariant is intimately related to the boundary of the hyperbolic Dehn surgery space of M.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-23.abs.htm

Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces

We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a topologically typical $Z$-periodic surface with boundary are recurrent.Comment: 34 pages, 13 figures. To be published in V. V. Kozlov's Festschrif

Recurrence in generic staircases

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure

Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz.Comment: 17 pages, 2 figure

Universal logic with encoded spin qubits in silicon

Qubits encoded in a decoherence-free subsystem and realized in exchange-coupled silicon quantum dots are promising candidates for fault-tolerant quantum computing. Benefits of this approach include excellent coherence, low control crosstalk, and configurable insensitivity to certain error sources. Key difficulties are that encoded entangling gates require a large number of control pulses and high-yielding quantum dot arrays. Here we show a device made using the single-layer etch-defined gate electrode architecture that achieves both the required functional yield needed for full control and the coherence necessary for thousands of calibrated exchange pulses to be applied. We measure an average two-qubit Clifford fidelity of $97.1 \pm 0.2\%$ with randomized benchmarking. We also use interleaved randomized benchmarking to demonstrate the controlled-NOT gate with $96.3 \pm 0.7\%$ fidelity, SWAP with $99.3 \pm 0.5\%$ fidelity, and a specialized entangling gate that limits spreading of leakage with $93.8 \pm 0.7\%$ fidelity

Effects of attention on the control of locomotion in individuals with chronic low back pain

<p>Abstract</p> <p>Background</p> <p>People who suffer from low back pain (LBP) exhibit an abnormal gait pattern, characterized by shorter stride length, greater step width, and an impaired thorax-pelvis coordination which may undermine functional walking. As a result, gait in LBP may require stronger cognitive regulation compared to pain free subjects thereby affecting the degree of automaticity of gait control. Conversely, because chronic pain has a strong attentional component, diverting attention away from the pain might facilitate a more efficient walking pattern.</p> <p>Methods</p> <p>Twelve individuals with LBP and fourteen controls participated. Subjects walked on a treadmill at comfortable speed, under varying conditions of attentional load: (a) no secondary task, (b) naming the colors of squares on a screen, (c) naming the colors of color words ("color Stroop task"), and (d) naming the colors of words depicting motor activities. Markers were attached to the thorax, pelvis and feet. Motion was recorded using a three-camera SIMI system with a sample frequency of 100 Hz. To examine the effects of health status and attention on gait, mean and variability of stride parameters were calculated. The coordination between thoracic and pelvic rotations was quantified through the mean and variability of the relative phase between those oscillations.</p> <p>Results</p> <p>LBP sufferers had a lower walking speed, and consequently a smaller stride length and lower mean thorax-pelvis relative phase. Stride length variability was significantly lower in the LBP group but no significant effect of attention was observed. In both groups gait adaptations were found under performance of an attention demanding task, but significantly more so in individuals with LBP as indicated by an interaction effect on relative phase variability.</p> <p>Conclusion</p> <p>Gait in LBP sufferers was characterized by less variable upper body movements. The diminished flexibility in trunk coordination was aggravated under the influence of an attention demanding task. This provides further evidence that individuals with LBP tighten their gait control, and this suggests a stronger cognitive regulation of gait coordination in LBP. These changes in gait coordination reduce the capability to deal with unexpected perturbations, and are therefore maladaptive.</p