Capacity for patterns and sequences in Kanerva's SDM as compared to other associative memory models

The information capacity of Kanerva's Sparse Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used, it is shown that the total information stored in these systems is proportional to the number connections in the network. The proportionality constant is the same for the SDM and Hopfield-type models independent of the particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences of spatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns

Naive Noncommutative Blowing Up

Let B(X,L,s) be the twisted homogeneous coordinate ring of an irreducible variety X over an algebraically closed field k with dim X > 1. Assume that c in X and s in Aut(X) are in sufficiently general position. We show that if one follows the commutative prescription for blowing up X at c, but in this noncommutative setting, one obtains a noncommutative ring R=R(X,c,L,s) with surprising properties. In particular: (1) R is always noetherian but never strongly noetherian. (2) If R is generated in degree one then the images of the R-point modules in qgr(R) are naturally in (1-1) correspondence with the closed points of X. However, both in qgr(R) and in gr(R), the R-point modules are not parametrized by a projective scheme. (3) qgr R has finite cohomological dimension yet H^1(R) is infinite dimensional. This gives a more geometric approach to results of the second author who proved similar results for X=P^n by algebraic methods.Comment: Latex, 42 page

Notes on implementation of sparsely distributed memory

The Sparsely Distributed Memory (SDM) developed by Kanerva is an unconventional memory design with very interesting and desirable properties. The memory works in a manner that is closely related to modern theories of human memory. The SDM model is discussed in terms of its implementation in hardware. Two appendices discuss the unconventional approaches of the SDM: Appendix A treats a resistive circuit for fast, parallel address decoding; and Appendix B treats a systolic array for high throughput read and write operations

CONSTITUTIONAL LAW-CONGRESSIONAL POWERS-VALIDITY OF THE 1953 SUBMERGED LANDS ACT

In 1947 and 1950 the Supreme Court held that the coastal states had no property interest in the submerged lands lying seaward from the low water mark, whether ownership of this land was held by the state prior to admission into the Union or not, and that the federal government had paramount rights in and power over this land, including the resources of the soil beneath it. In 1953 Congress passed, and the President signed, the Submerged Lands Act, which vested in the coastal states title to and proprietary power over this land. Alabama and Rhode Island petitioned the Court for leave to file complaints against two of the coastal states as to actions taken and proposed to be taken under this act. Held, per curiam, two justices dissenting, motion denied. Under article IV, section 3, clause 2 of the Constitution, Congress has an unlimited power to dispose of any kind of property belonging to the United States. Alabama v. Texas, 347 U.S. 272, 74 S.Ct. 481 (1954)

Agency - Apparent Authority of Sales Agent

Defendant\u27s agent, a consignee of automobiles for sale, received from plaintiff a used truck, and agreed to apply the proceeds from the sale of the truck to the purchase price of a new automobile, to be sold and delivered to plaintiff when available. Defendant\u27s agent sold the truck and absconded with the proceeds from such sale. Plaintiff sued for the value of the truck, and the lower court rendered judgment in his favor. On appeal, held, affirmed. The acts of the agent bound the defendant, although the agency contract gave only express authority to sell new automobiles. Correa v. Duality Motor Co., (Cal. App. 1953) 257 P. (2d) 738

Constitutional Law- Zoning - Private High Schools Excluded from Zone in Which Public High Schools Permitted

Among the uses permitted in the A residence zone by the Wauwatosa, Wisconsin zoning ordinance were (e) Public Schools and Private Elementary Schools. The city building inspector denied to plaintiff, a private, non-profit religious corporation, a permit for the construction of a private high school in that zone. Plaintiff brought an action in mandamus to compel the issuance of such a permit, alleging that the ordinance deprived plaintiff of property without due process of law, and denied to it the equal protection of the laws guaranteed by the Fourteenth Amendment. The lower court granted the writ. On appeal, held, reversed. The detrimental effect which the proposed school would have on the affected residential neighborhood justified making it a subject of the zoning power. Furthermore, the distinction made between public and private high schools was justified by the lesser contribution to the general welfare made by the private high school. State ex rel. Wisconsin Lutheran High School Conference v. Sinar, 267 Wis. 91, 65 N.W. (2d) 43 (1954)

Negligence - Duties of Railroad - Landowner Toward Frequent Trespasser - Limitations on Rights of Trespasser

The duties of a landowner toward one who enters the land without consent may no longer be determined, in many cases, by merely stating the fact that the intruder is a trespasser whose presence is unknown to the landowner. This comment will discuss an area in which the relationship of landowner and trespasser inter se has been greatly altered, and will deal in particular with a class of cases which serve to limit the expanded rights of the trespasser