Essays on geography and diseases

This dissertation explores how diseases contributed to shape historical institutions and how health and diseases are still affecting modern comparative development. The overarching goal of this investigation is to identify the channels linking geographic suitability to diseases and the emergence of historical and modern insitutions, while tackling the endogenenity problems that traditionally undermine this literature. I attempt to do so by taking advantage of the vast amount of newly available historical data and of the richness of data accessible through the geographic information system (GIS). The first chapter of my thesis, 'Side Effects of Immunities: The African Slave Trade', proposes and test a novel explanation for the origins of slavery in the tropical regions of the Americas. I argue that Africans were especially attractive for employment in tropical areas because they were immune to many of the diseases that were ravaging those regions. In particular, Africans' resistance to malaria increased the profitability of slaves coming from the most malarial parts of Africa. In the second chapter of my thesis, 'Caste Systems and Technology in Pre-Modern Societies', I advance and test the hypothesis that caste systems, generally viewed as a hindrance to social mobility and development, had been comparatively advantageous at an early stage of economic development. In the third chapter, 'Malaria as Determinant of Modern Ethnolinguistic Diversity', I conjecture that in highly malarious areas the necessity to adapt and develop immunities specific to the local disease environment historically reduced mobility and increased isolation, thus leading to the formation of a higher number of different ethnolinguistic groups. In the final chapter, 'Malaria Risk and Civil Violence: A Disaggregated Analysis for Africa', I explore the relationship between malaria and violent conflicts. Using georeferenced data for Africa, the article shows that violent events are more frequent in areas where malaria risk is higher.

Absolute Hodge cycles and Deligne's principle b

I cicli di Hodge assoluti sono stati utilizzati da Deligne per dividere la congettura di Hodge in due sotto-congetture. La prima dice che tutte le classi di Hodge su una varietà complessa proiettiva liscia sono assolute, la seconda che le classi assolute sono algebriche. Deligne ha dato risposta affermativa alla prima sottocongettura nel caso delle varietà abeliane. La dimostrazione si basa su due teoremi, conosciuti rispettivamente come Principio A e Principio B. In questo lavoro vengono presentate la teoria delle classi di Hodge assolute e la dimostrazione del Principio B.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Comparing skew Schur functions: a quasisymmetric perspective

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.

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.