A Coding Theoretic Study on MLL proof nets

Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area of mathematics, in which there is an interplay between many branches of mathematics, e.g., abstract algebra, combinatorics, discrete geometry, information theory, etc. In this paper we propose a novel approach for analyzing proof nets of Multiplicative Linear Logic (MLL) by coding theory. We define families of proof structures and introduce a metric space for each family. In each family, 1. an MLL proof net is a true code element; 2. a proof structure that is not an MLL proof net is a false (or corrupted) code element. The definition of our metrics reflects the duality of the multiplicative connectives elegantly. In this paper we show that in the framework one error-detecting is possible but one error-correcting not. Our proof of the impossibility of one error-correcting is interesting in the sense that a proof theoretical property is proved using a graph theoretical argument. In addition, we show that affine logic and MLL + MIX are not appropriate for this framework. That explains why MLL is better than such similar logics.Comment: minor modification

Fast rate of convergence in high dimensional linear discriminant analysis

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated to the geometric parameters defining the used discrimination rule

On the existence of zero-sum subsequences of distinct lengths

In this paper, we obtain a characterization of short normal sequences over a finite Abelian p-group, thus answering positively a conjecture of Gao for a variety of such groups. Our main result is deduced from a theorem of Alon, Friedland and Kalai, originally proved so as to study the existence of regular subgraphs in almost regular graphs. In the special case of elementary p-groups, Gao's conjecture is solved using Alon's Combinatorial Nullstellensatz. To conclude, we show that, assuming every integer satisfies Property B, this conjecture holds in the case of finite Abelian groups of rank two.Comment: 10 pages, to appear in Rocky Mountain Journal of Mathematic

Plugin procedure in segmentation and application to hyperspectral image segmentation

In this article we give our contribution to the problem of segmentation with plug-in procedures. We give general sufficient conditions under which plug in procedure are efficient. We also give an algorithm that satisfy these conditions. We give an application of the used algorithm to hyperspectral images segmentation. Hyperspectral images are images that have both spatial and spectral coherence with thousands of spectral bands on each pixel. In the proposed procedure we combine a reduction dimension technique and a spatial regularisation technique. This regularisation is based on the mixlet modelisation of Kolaczyck and Al

Phelps Lake and Jim Burt: Two Middle Woodland Period Mounds in Northwestern Louisiana

Clarence Webb defined the pre-Caddoan Bellevue focus on the basis of investigations at several isolated mounds located in upland settings in northwestern Louisiana. With the exception of the Bellevue Site (16B04), little detailed information is available about these mounds. Most were excavated many years ago and few notes, photographs, or other records exist This paper describes the results of recent cleaning of an old excavation trench through one of the Bellevue focus sites the Phelps Lake Mound (16B024). The work has provided a relatively detailed look at the mound strata. A radiocarbon assay on a sample of charcoal underlying the mound constitutes one of the few chronometric dates from a Bellevue focus context. Also discussed briefly is the Jim Burt Site (16B023), where a radiocarbon assay was obtained on charcoal recovered near the mound

Recent Investigations at the Mounds Plantation Site (16CD12), Caddo Parish, Louisiana

Dr. Montroville Wilson Dickeson, born in Philadelphia in 1810, was a medical doctor, taxidermist and avid collector of fossils. Between 1837 and 1844 he pursued another interest—excavating Indian burial mounds in the Ohio and Mississippi River valleys. He claimed to have “opened up” more than a thousand mounds and collected more than 40,000 objects. He also made drawings of the mounds and later provided these to an artist by the name of John J. Egan, who, about 1850, converted the drawings into a series of large paintings on huge canvases. Dickeson toured the country in 1852 allowing the public to view the canvasses and his artifact collections for a fee of 25 cents. The panorama, titled “Monumental Grandeur of the Mississippi Valley”, was nine feet high, 400 feet long, and consisted of 27 scenes. The canvasses later were curated at the University Museum, University of Pennsylvania until 1953 when purchased by the St. Louis Art Museum where they remain today. Dickeson’s lecture notes refer to Scene 21 as follows: “The following picture shows a group of connected mounds in Caddo Parish, in Northwestern Louisiana, with some of the aboriginal inhabitants of the region . . .” The scene depicts a cluster of nine mounds, some of which are connected by low earthen walls. In the background are mountains, and a group of Indians with elaborate headdresses are shown in front of tents. Similar mountains and the same Indian scene appear in other segments of the Mississippi Panorama and are understandable in light of the Romantic artistic style of the times, as well as the fact that the panorama was part of a show intended to evoke wonder and awe in its audience. Today we know of only one place in Caddo Parish where there is a cluster of at least nine mounds. Located on the western side of the Red River, north of the present city of Shreveport, is the Mounds Plantation Site (16CD12), the single largest Caddo ceremonial center in northwestern Louisiana. It seems fitting that the earliest reference that we have to a prehistoric site in northwest Louisiana likely pertains to Mounds Plantation, a place of primary importance to its ancient Caddo inhabitants, as well as to modern archaeological research

Comments on Caddo Origins in Northwest Louisiana

This paper presents some of my thoughts on the issue of Caddo origins from the perspective of the Red River drainage in northwest Louisiana. These ideas were assembled prior to the Caddo discussion group meeting held in December 2008 and have been only slightly modified here. The paper was not given as a formal presentation, but I attempted to introduce the main points during the group discussion. Development of better chronological controls is crucial for addressing problems of Caddo origins, and I discuss this issue first. Although much has been settled since the early Krieger-Ford discussions, a finer-grained chronology is necessary to answer questions that are now of interest. We remain largely dependent on our understanding of changes in ceramic assemblages and how we can tie these to chronometric scales based primarily on radiocarbon dating. I next review the cultural taxonomic units that have been used to classify the pre-Caddo archaeological record in the Trans-Mississippi South. Rather than taking the view that one or more of these cultural entities transformed into Caddo culture, I suggest that Caddo origins might be better viewed as the development of social and economic behaviors that linked relatively small-scale social units previously only loosely and sporadically associated. I then discuss the possible importance of the development of ceremonial centers, the appearance of elite mortuary traits, and the circulation of finely engraved ceramic vessels for understanding changes in social and economic integration that took place in the Trans- Mississippi South between approximately A.D. 900 and A.D. 1050. Finally, I offer a list of some basic questions that I feel are important for furthering our understanding of Caddo origins

Punishing Pharmaceutical Companies for Unlawful Promotion of Approved Drugs: Why the False Claims Act is the Wrong Rx

This article criticizes the shift in focus from correction and compliance to punishment of pharmaceutical companies allegedly violating the Food, Drug, & Cosmetic Act (FD&C Act) prohibitions on unlawful drug promotion. Traditionally, the Food and Drug Administration (FDA) has addressed unlawful promotional activities under the misbranding and new drug provisions of the FD&C Act. Recently though, the Justice Department (DOJ) has expanded the purview of the False Claims Act to include the same allegedly unlawful behavior on the theory that unlawful promotion “induces” physicians to prescribe drugs that result in the filing of false claims for reimbursement. Unchecked and unchallenged, the DOJ has negotiated criminal and civil settlements with individual pharmaceutical companies ranging from just under ten to hundreds of millions of dollars. In part, companies settle these cases to avoid the potential loss of revenue associated with the exclusion regime administered by the U.S. Department of Health and Human Services, under which companies risk losing the right to participate in federal health care programs. Even more disturbing, these settlements allow DOJ to circumvent judicial review of its enforcement approach, preventing any type of accountability for its legal theories or procedures. This article discusses the traditional enforcement methods employed by the FDA as well as the more recent DOJ prosecutions under the False Claims Act. Although it concludes that the FD&C Act should provide the sole means for prosecuting unlawful drug promotion, it also suggests that when prosecuting pharmaceutical companies under either Act, the government must avoid the temptation to mine companies for large settlements in lieu of developing a more coherent and responsible enforcement strategy

Sites in Northern Louisiana with Major Collections of Historic Caddo and Other Native American Pottery

Archaeological sites in northern Louisiana that date to the 18th and 19th centuries which have yielded significant amounts of Native American pottery are plotted on the accompanying map, and briefly summarized below. A common feature of ceramic collections from these sites is the prevalence of shell temper, a trait that is rare prior to the late 17th century in the region. The earliest contexts probably date from the late 17th to the early 18th centuries and include utilitarian types that were common during the Late Caddo period (ca. A.D. 1500-1700). By the middle 18th century, these types apparently were no longer used as shown by their absence at Los Adaes and sites along Cane River. Many traditional Caddo vessel forms (such as bottles and carinated bowls) appear to have dropped out of use during the late 18th century. Several early 19th century sites that relate to occupants of the ethnically-mixed Bayou Pierre community north of Natchitoches contain Native American shell-tempered pottery, but represented vessel forms are similar to the Colonoware that is widespread in the eastern U.S. A small number of engraved and incised sherds have been recovered at these sites, but it is possible that they are from earlier Caddo occupations. Groups that originated east of the Mississippi Valley moved into northern Louisiana during the late 18th century, and new types such as Zimmerman Black, Chickashae Red, Chickashae Combed, and Chattahoochee Roughened appear in the archaeological record. Native American pottery disappears from the archaeological record in the region by 1830