Equazioni stocastiche lineari e disuguaglianza di Harnack

In questo elaborato si presentano alcuni risultati relativi alle equazioni differenziali stocastiche (SDE) lineari. La soluzione di un'equazione differenziale stocastica lineare è un processo stocastico con distribuzione multinormale in generale degenere. Al contrario, nel caso in cui la matrice di covarianza è definita positiva, la soluzione ha densità gaussiana Γ. La Γ è inoltre la soluzione fondamentale dell'operatore di Kolmogorov associato alla SDE. Nel primo capitolo vengono presentate alcune condizioni necessarie e sufficienti che assicurano che la matrice di covarianza sia definita positiva nel caso, più semplice, in cui i coefficienti della SDE sono costanti, e nel caso in cui questi sono dipendenti dal tempo. A questo scopo gioca un ruolo fondamentale la teoria del controllo. In particolare la condizione di Kalman fornisce un criterio operativo per controllare se la matrice di covarianza è definita positiva. Nel secondo capitolo viene presentata una dimostrazione diretta della disuguaglianza di Harnack utilizzando una stima del gradiente dovuta a Li e Yau. Le disuguaglianze di Harnack sono strumenti fondamentali nella teoria delle equazioni differenziali a derivate parziali. Nel terzo capitolo viene proposto un esempio di applicazione della disuguaglianza di Harnack in finanza. In particolare si osserva che la disuguaglianza di Harnack fornisce un limite superiore a priori del valore futuro di un portafoglio autofinanziante in funzione del capitale iniziale.

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.

Inflammasome-dependent IFN-γ drives pathogenesis in Streptococcus pneumoniae meningitis

The pathology associated with Streptococcus pneumoniae meningitis results largely from activation of immune-associated pathways. We systematically investigated the production of IFN subtypes, as well as their influence on pathology, in a mouse model of S. pneumoniae meningitis. Despite the occurrence of a mixed IFN type I/II gene signature, no evidence for production or involvement of type I IFNs in disease progression was found. In contrast, type II IFN (IFN-γ) was strongly induced, and IFN-γ(-/-) mice were significantly protected from severe disease. Using intracellular cytokine staining and targeted cell-depletion approaches, NK cells were found to be the dominant source of IFN-γ. Furthermore, production of IFN-γ was found to be dependent upon ASC and IL-18, indicating that an ASC-dependent inflammasome pathway was responsible for mediating IFN-γ induction. The influence of IFN-γ gene deletion on a range of processes known to be involved in bacterial meningitis pathogenesis was examined. Although neutrophil numbers in the brain were similar in infected wild-type and IFN-γ(-/-) mice, both monocyte recruitment and CCL2 production were less in infected IFN-γ(-/-) mice compared with infected wild-type controls. Additionally, gene expression of NO synthase was strongly diminished in infected IFN-γ(-/-) mice compared with infected controls. Finally, bacterial clearance was enhanced in IFN-γ(-/-) mice, although the underlying mechanism remains unclear. Together, these data suggest that inflammasome-dependent IFN-γ contributes via multiple pathways to pathology during S. pneumoniae meningitis.

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.

Interaction of the solar wind with them Moon: An overview on the results from the SARA experiment aboard Chandrayaan-1

The results from the Sub-keV Atom Reflecting Analyzer (SARA) experiment onboard Chandrayaan-1 have revealed several hitherto unknown and interesting aspects about the interaction of solar wind with the Moon. The SARA experiment had two sensors — CENA and SWIM. The Chandrayaan-1 energetic neutrals analyzer (CENA), detected energetic neutral atoms (ENAs), and the Solar Wind Monitor (SWIM) measured ions of solar wind origin. In this review, we summarize the observations made by the SARA experiment, which are: (1) substantial (~20%) and sustained backscattering of solar wind protons from lunar surface as energetic neutral hydrogen,1 (2) minimagnetosphere around magnetic anomalies on Moon using the backscattered ENAs,2 (3) reflection of solar wind protons from the Moon surface,3 (4) huge (~50%) deflection of solar wind protons over strong magnetic anomalies,4 and (5) presence of protons in the near-lunar plasma wake.5 These results have implications on the lunar plasma environment, implantation of solar wind hydrogen on lunar surface, and behavior of small scale magnetic anomalies on planetary bodies. The SARA observations suggest that similar processes may happen on other airless bodies covered with regolith in the solar system as well as in extra-solar system. This paper presents a review of the results obtained from the SARA observation.

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.

Laribacter hongkongensis: a potential cause of infectious diarrhea

In this study, we describe the isolation of Laribacter hongkongensis, a recently described genus and species of bacterium, in pure culture on charcoal cefoperazone deoxycholate agar from the stool of six patients with diarrhea. Three patients were residents of Hong Kong, and three of Switzerland. In none of the stool samples obtained from these six patients was Salmonella, Shigella, enterohemorrhagic Escherichia coli, Vibrio, Aeromonas, Plesiomonas, or Campylobacter recovered. Rotavirus antigen detection, electron microscopic examination for viruses, and microscopic examinations for ova and cysts were all negative for the stool samples obtained from the three patients in Hong Kong. Enterotoxigenic E. coli was recovered from one of the patients in Hong Kong. Unlike L. hongkongensis type strain HKU1, all the six strains were motile with bipolar flagellae. Sequencing of the 16S ribosomal RNA genes of the six strains showed that they all had sequences with only 0-2 base differences to that of the type strain. Pulsed field gel electrophoresis of the SpeI digested genomic DNA of the six isolates and that of the type strain revealed that the seven isolates were genotypically unrelated strains. More extensive epidemiologic studies should be carried out to ascertain the causative association between L. hongkongensis and diarrhea and to define the reservoir and modes of transmission of L. hongkongensis.

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.