Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

Statistics of the received power for free space optical channels

Free space optical (FSO) communication links can experience extreme signal degradation due to atmospheric turbulence induced spatial and temporal irradiance fuctuations (scintillation) in the laser wavefront. In addition, turbulence can cause the laser beam centroid to wander resulting in power fading, and sometimes complete loss of the signal. Spreading of the laser beam and jitter are also artifacts of atmospheric turbulence. To accurately predict the signal fading that occurs in a laser communication system and to get a true picture of how this affects crucial performance parameters like bit error rate (BER) it is important to analyze the probability density function (PDF) of the integrated irradiance fuctuations at the receiver. In addition, it is desirable to find a theoretical distribution that accurately models these ?uctuations under all propagation conditions. The PDF of integrated irradiance fuctuations is calculated from numerical wave-optic simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to very strong. Our results show that the gamma-gamma PDF provides a good fit to the simulated data distribution for all aperture sizes studied from weak through moderate scintillation. In strong scintillation, the gamma-gamma PDF is a better fit to the distribution for point-like apertures and the lognormal PDF is a better fit for apertures the size of the atmospheric spatial coherence radius ρ0 or larger. In addition, the PDF of received power from a Gaussian laser beam, which has been adaptively compensated at the transmitter before propagation to the receiver of a FSO link in the moderate scintillation regime is investigated. The complexity of the adaptive optics (AO) system is increased in order to investigate the changes in the distribution of the received power and how this affects the BER. For the 10 km link, due to the non-reciprocal nature of the propagation path the optimal beam to transmit is unknown. These results show that a low-order level of complexity in the AO provides a better estimate for the optimal beam to transmit than a higher order for non-reciprocal paths. For the 20 km link distance it was found that, although minimal, all AO complexity levels provided an equivalent improvement in BER and that no AO complexity provided the correction needed for the optimal beam to transmit. Finally, the temporal power spectral density of received power from a FSO communication link is investigated. Simulated and experimental results for the coherence time calculated from the temporal correlation function are presented. Results for both simulation and experimental data show that the coherence time increases as the receiving aperture diameter increases. For finite apertures the coherence time increases as the communication link distance is increased. We conjecture that this is due to the increasing speckle size within the pupil plane of the receiving aperture for an increasing link distance.

Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.

Ctp1 and the MRN-complex are required for endonucleolytic Rec12 removal with release of a single class of oligonucleotides in fission yeast

DNA double-strand breaks (DSBs) are formed during meiosis by the action of the topoisomerase-like Spo11/Rec12 protein, which remains covalently bound to the 5' ends of the broken DNA. Spo11/Rec12 removal is required for resection and initiation of strand invasion for DSB repair. It was previously shown that budding yeast Spo11, the homolog of fission yeast Rec12, is removed from DNA by endonucleolytic cleavage. The release of two Spo11 bound oligonucleotide classes, heterogeneous in length, led to the conjecture of asymmetric cleavage. In fission yeast, we found only one class of oligonucleotides bound to Rec12 ranging in length from 17 to 27 nucleotides. Ctp1, Rad50, and the nuclease activity of Rad32, the fission yeast homolog of Mre11, are required for endonucleolytic Rec12 removal. Further, we detected no Rec12 removal in a rad50S mutant. However, strains with additional loss of components localizing to the linear elements, Hop1 or Mek1, showed some Rec12 removal, a restoration depending on Ctp1 and Rad32 nuclease activity. But, deletion of hop1 or mek1 did not suppress the phenotypes of ctp1Delta and the nuclease dead mutant (rad32-D65N). We discuss what consequences for subsequent repair a single class of Rec12-oligonucleotides may have during meiotic recombination in fission yeast in comparison to two classes of Spo11-oligonucleotides in budding yeast. Furthermore, we hypothesize on the participation of Hop1 and Mek1 in Rec12 removal.

Corporate dividencs and seasoned equity issues: an empirical investigation

This paper investigates whether managers rely on dividends to obtain a higher price in a stock offering and whether the stock price reaction to dividend and offering announcements justifies such a coordination. The evidence does not support either conjecture. Issuing firms are not more likely to pay or increase dividends than nonissuing forms. Moreover, there is little evidence that firms time stock offering announcements right after dividend declarations to befefit from the attendant information disclosure. The analysis of dividend and stock offering announcement effects suggests few if any benefits from linking divbidend and stock offering announcements.

Is there a ‚Depth versus Participation‘ Dilemma in International Cooperation?

Much of the International Relations literature assumes that there is a “depth versus participation” dilemma in international politics: shallower international agreements attract more countries and greater depth is associated with less participation. We argue that this conjecture is too simple and probably misleading because the depth of any given cooperative effort is in fact multidimensional. This multidimensionality manifests itself in the design characteristics of international agreements: in particular, the specificity of obligations, monitoring and enforcement mechanisms, dispute settlement mechanisms, positive incentives (assistance), and organizational structures (secretariats). We theorize that the first three of these design characteristics have negative and the latter three have positive effects on participation in international cooperative efforts. Our empirical testing of these claims relies on a dataset that covers more than 200 global environmental treaties. We find a participation-limiting effect for the specificity of obligations, but not for monitoring and enforcement. In contrast, we observe that assistance provisions in treaties have a significant and substantial positive effect on participation. Similarly, dispute settlement mechanisms tend to promote treaty participation. The main implication of our study is that countries do not appear to stay away from agreements with monitoring and enforcement provisions, but that the inclusion of positive incentives and dispute settlement mechanisms can promote international cooperation. In other words, our findings suggest that policymakers do not necessarily need to water down global treaties in order to obtain more participation.

Evidence of species-specific neighborhood effects in the dipterocarpaceae of a Bornean rain forest

Although accumulating evidence indicates that local intraspecific density-dependent effects are not as rare in species-rich communities as previously suspected, there are still very few detailed and systematic neighborhood analyses of species-rich communities. Here, we provide such an analysis with the overall goal of quantifying the relative importance of inter- and intraspecific interaction strength in a primary, lowland dipterocarp forest located at Danum, Sabah, Malaysia. Using data on 10 abundant overstory dipterocarp species from two 4-ha permanent plots, we evaluated the effects of neighbors on the absolute growth rate of focal trees (from 1986 to 1996) over increasing neighborhood radii (from 1 to 20 m) with multiple regressions. Only trees 10 cm to < 100 cm girth at breast height in 1986 were considered as focal trees. Among neighborhood models with one neighbor term, models including only conspecific larger trees performed best in five out of 10 species. Negative effects of conspecific larger neighbors were most apparent in large overstory species such as those of the genus Shorea. However, neighborhood models with separate terms and radii for heterospecific and conspecific neighbors accounted for more variability in absolute growth rates than did neighborhood models with one neighbor term. The conspecific term was significant for nine out of 10 species. Moreover, in five out of 10 species, trees without conspecific neighbors had significantly higher absolute growth rates than trees with conspecific neighbors. Averaged over the 10 species, trees without conspecific neighbors grew 32.4 cm(2) in basal area from 1986 to 1996, whereas trees with conspecific neighbors only grew 14.7 cm(2) in basal area, although there was no difference in initial basal area between trees in the two groups. Averaged across the six species of the genus Shorea, negative effects of conspecific larger trees were significantly stronger than for heterospecific larger neighbors. Thus, high local densities within neighborhoods of 20 m may lead to strong intraspecific negative and, hence, density-dependent, effects even in species rich communities with low overall densities at larger spatial scales. We conjecture that the strength of conspecific effects may be correlated with the degree of host specificity of ectomycorrhizae.

Loose but normal: a semantic association study.

An abnormal facilitation of the spreading activation within semantic networks is thought to under-lie schizophrenics' remote associations and referential ideas. In normal subjects, elevated magical ideation (MI) has also been associated with a style of thinking similar to that of schizotypal subjects. We thus wondered whether normal subjects with a higher MI score would judge "loose associations" as being more closely related than do subjects with a lower MI score. In two experiments, we investigated whether judgments of the semantic distance between stimulus words varied as a function of MI. In the first experiment, random word pairs of two word classes, animals and fruits, were presented. Subjects had to judge the semantic distance between word pairs. In the second experiment, sets of three words were presented, consisting of a pair of indirectly related, or unrelated nouns plus a third noun. Subjects had to judge the semantic distance of the third noun to the word pair The results of both experiments showed that higher MI subjects considered unrelated words as more closely associated than did lower MI subjects. We conjecture that for normal subjects high on MI "loose associations" may not be loose after all. We also note that the tendency to link uncommon, nonobvious, percepts may not only be the basis of paranormal and paranoid ideas of reference, but also a prerequisite of creative thinking.

Brain damage and addictive behavior: a neuropsychological and electroencephalogram investigation with pathologic gamblers.

BACKGROUND Gambling is a form of nonsubstance addiction classified as an impulse control disorder. Pathologic gamblers are considered healthy with respect to their cognitive status. Lesions of the frontolimbic systems, mostly of the right hemisphere, are associated with addictive behavior. Because gamblers are not regarded as "brain-lesioned" and gambling is nontoxic, gambling is a model to test whether addicted "healthy" people are relatively impaired in frontolimbic neuropsychological functions. METHODS Twenty-one nonsubstance dependent gamblers and nineteen healthy subjects underwent a behavioral neurologic interview centered on incidence, origin, and symptoms of possible brain damage, a neuropsychological examination, and an electroencephalogram. RESULTS Seventeen gamblers (81%) had a positive medical history for brain damage (mainly traumatic head injury, pre- or perinatal complications). The gamblers, compared with the controls, were significantly more impaired in concentration, memory, and executive functions, and evidenced a higher prevalence of non-right-handedness (43%) and, non-left-hemisphere language dominance (52%). Electroencephalogram (EEG) revealed dysfunctional activity in 65% of the gamblers, compared with 26% of controls. CONCLUSIONS This study shows that the "healthy" gamblers are indeed brain-damaged. Compared with a matched control population, pathologic gamblers evidenced more brain injuries, more fronto-temporo-limbic neuropsychological dysfunctions and more EEG abnormalities. The authors thus conjecture that addictive gambling may be a consequence of brain damage, especially of the frontolimbic systems, a finding that may well have medicolegal consequences.

Invitation à la topologie algébrique. Tome II. Cohomologie, variétés

Ce Tome II introduit la cohomologie, qui est une théorie duale de l'homologie, et examine les liens avec cette dernière ainsi que les divers produits construits sur les modules d'homologie et de cohomologie. Nous étudions en détail les variétés topologiques avec ou sans bord, définissons sur celles-ci au moyen de l'homologie une notion d'orientation et la comparons avec les définitions classiques d'orientation pour les variétés différentiables ou triangulables. Nous exposons les théorèmes de dualité de Poincaré, Alexander et Lefschetz et en déduisons les propriétés des formes d'intersection et de la signature des variétés. Le dernier chapitre du livre présente les résultats fondamentaux concernant la différentiabilité et la triangulabilité des variétés, obtenus depuis les années soixante du siècle dernier, tant en grandes dimensions qu'en dimension quatre. Nous discutons également la conjecture de Poincaré classique et ses généralisations. Bien que des démonstrations complètes de ces résultats soient hors de portée d'un ouvrage tel que le nôtre, nous nous sommes attachés à rendre leurs énoncés compréhensibles. Cette vue d'ensemble, et les références à la littérature qui l'accompagnent, fournissent une introduction aux développements récents dans ce riche domaine de la topologie.

Guaranteed resonance enclosures and exclosures for atoms and molecules

In this paper, we confirm, with absolute certainty, a conjecture on a certain oscillatory behaviour of higher auto-ionizing resonances of atoms and molecules beyond a threshold. These results not only definitely settle a more than 30 year old controversy in Rittby et al. (1981 Phys. Rev. A 24, 1636–1639 (doi:10.1103/PhysRevA.24.1636)) and Korsch et al. (1982 Phys. Rev. A 26, 1802–1803 (doi:10.1103/PhysRevA.26.1802)), but also provide new and reliable information on the threshold. Our interval-arithmetic-based method allows one, for the first time, to enclose and to exclude resonances with guaranteed certainty. The efficiency of our approach is demonstrated by the fact that we are able to show that the approximations in Rittby et al. (1981 Phys. Rev. A 24, 1636–1639 (doi:10.1103/PhysRevA.24.1636)) do lie near true resonances, whereas the approximations of higher resonances in Korsch et al. (1982 Phys. Rev. A 26, 1802–1803 (doi:10.1103/PhysRevA.26.1802)) do not, and further that there exist two new pairs of resonances as suggested in Abramov et al. (2001 J. Phys. A 34, 57–72 (doi:10.1088/0305-4470/34/1/304)).

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

Calcareous nannofossils in sediments of the Japan Sea

Preliminary results of the biostratigraphic analysis of calcareous nannofossils recovered from Ocean Drilling Program Leg 128, Sites 798 and 799, provide clues to the Quaternary oceanography of the Japan Sea. The distribution of calcareous nannofossils from the Quaternary sediments at Site 798 (903 m water depth) may record the position of an Oceanographic frontal boundary between warm water derived from a branch of the Kuroshio Current as it entered the Japan Sea through the Tsushima Straits to the south, and colder water introduced into the western portion of the Japan Sea derived from the winter chilling of northern Japan Sea surface waters. This Oceanographic front probably oscillated north-south over Site 798 in response to glacial/interglacial cycles, or perhaps to some other climatic event or combination of events unique to the Japan Sea. During the last 1.5 m.y., six major intervals are recognized when the Oceanographic front may have been north of Site 798 separated by five major intervals when the frontal boundary may have been south of the site. These migrations were centered around approximately 0.125, 0.29, 0.56, 0.62, 0.85, 0.91, 0.98, 1.0, 1.11, and 1.5 Ma, which correspond to the boundaries separating nannofossil-rich sediments from barren or nearly barren, low-carbonate intervals. Nannofossil-rich intervals may represent times when the frontal boundary was north of Site 798, and the site was above the CCD. Barren or nearly barren intervals represent times when the frontal boundary may have been south of Site 798 and the CCD was probably higher. The distribution of calcareous nannofossils at Site 799 (2073 m water depth) appears to be controlled more by the depth of the CCD than by any climatic effects. The FOD (first occurrence datum) of Emiliania huxleyi, the LOD (last occurrence datum) of Psuedoemiliania lacunosa, Helicosphaera sellii, Calcidiscus macintyrei (10 ?m), and the FOD and LOD of Reticulofenestra asanoi are recognized from Site 798 cores. The LOD of P. lacunosa is observed in sediments from Site 799. Only in the sediments younger than 1.5 Ma are the nannofossils from Sites 798 and 799 preserved well enough and sufficiently numerous for age dating and paleoceanographic conjecture. In-situ dissolution in older sediments at both sites precludes any dating or paleoenvironmental interpretations.

Ruralia, tradicionalismo y población en la Puna de Jujuy durante el siglo XX

El crecimiento de la población puneña durante el siglo XX resulta de la evolución de tres circunstancias centrales. La primera consiste en que la sociedad puneña, especialmente la rural, ha sido, y en buena medida lo es, una sociedad tradicional, es decir, no moderna, preindustrial, con estructura social poco diferenciada, con pautas culturales diferenciales. La otra se relaciona con el proceso de articulación entre esa sociedad tradicional y la moderna, capitalista, extra-puneña. La conjetura es que la consolidación del capitalismo en el Noroeste argentino a partir del último tercio del siglo XIX no desplazó ni reemplazó a la sociedad tradicional: convivió con ella durante décadas generando cambios sustanciales en numerosos aspectos. La tercera tiene que ver con la acción del Estado: al menos durante las primeras décadas del XX operó en el contexto del positivismo, asociado con el concepto de desarrollo no lejano al de progreso. A través del progreso, la sociedad tradicional se transforma en una sociedad racional, secular, con estructuras sociales diferenciadas.

El método de Freud y la tradición hermenéutica en psicoanálisis

Este trabajo aborda críticamente los argumentos fundamentales de un sector de teorizaciones y prácticas psicoanalíticas que han sido agrupadas bajo la denominación de "tradición hermenéutica", basándose en dos aspectos: primero, atendiendo a la distancia que dichos argumentos mantienen respecto de la propuesta original de Freud; segundo, analizando los supuestos y valores epistémicos que han orientado (explícita e implícitamente) a tales perspectivas. Posteriormente al abordaje crítico, se conjeturan argumentos tendientes a trascender o reenfocar algunos problemas metodológicos de la investigación y práctica psicoanalítica, tales como la conceptualización y formalización de la acción causal, la validación de las conjeturas (metapsicológicas y clínicas) y el lugar de las formalizaciones teóricas en la clínica