Global GacA-steered control of cyanide and exoprotease production in Pseudomonas fluorescens involves specific ribosome binding sites

The conserved two-component regulatory system GacS/GacA determines the expression of extracellular products and virulence factors in a variety of Gram-negative bacteria. In the biocontrol strain CHA0 of Pseudomonas fluorescens, the response regulator GacA is essential for the synthesis of extracellular protease (AprA) and secondary metabolites including hydrogen cyanide. GacA was found to exert its control on the hydrogen cyanide biosynthetic genes (hcnABC) and on the aprA gene indirectly via a posttranscriptional mechanism. Expression of a translational hcnA′-′lacZ fusion was GacA-dependent whereas a transcriptional hcnA-lacZ fusion was not. A distinct recognition site overlapping with the ribosome binding site appears to be primordial for GacA-steered regulation. GacA-dependence could be conferred to the Escherichia coli lacZ mRNA by a 3-bp substitution in the ribosome binding site. The gene coding for the global translational repressor RsmA of P. fluorescens was cloned. RsmA overexpression mimicked partial loss of GacA function and involved the same recognition site, suggesting that RsmA is a downstream regulatory element of the GacA control cascade. Mutational inactivation of the chromosomal rsmA gene partially suppressed a gacS defect. Thus, a central, GacA-dependent switch from primary to secondary metabolism may operate at the level of translation.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Formal group laws and hypergraph colorings

Thesis (Ph.D.)--University of Washington, 2016-06

Diplacanthid acanthodians from the Aztec Siltstone (late Middle Devonian) of southern Victoria Land, Antartica

One articulated and several partial, semi-articulated specimens of acanthodians were collected in 1970 from the freshwater deposits of the Aztec Siltstone (Middle Devonian; Givetian), Portal Mountain, southern Victoria Land, Antarctica, during a Victoria University of Wellington Antarctic Expedition. The Portal Mountain fish fauna, preserved in a finely laminated, non-calcareous siltstone, includes acanthodians, palaeoniscoids, and bothriolepid placoderms. The articulated acanthodian specimens are the most complete fossil fish remains documented so far from the Aztec assemblage, which is the most diverse fossil vertebrate fauna known from Antarctica. They are described as a new taxon, Milesacanthus antarctica gen. et sp. nov., which is assigned to the family Diplacanthidae. Its fin spines show some similarities to spine fragments named Byssacanthoides debenhami from glacial moraine at Granite Harbour, Antarctica, and much larger spines named Antarctonchus glacialis from outcrops of the Aztec Siltstone in the Boomerang Range, southern Victoria Land. Both of these are reviewed, and retained as form taxa for isolated spines. Various isolated remains of fin spines and scales are described from Portal Mountain and Mount Crean (Lashly Range), and referred to Milesacanthus antarctica gen. et sp. nov. The histology of spines and scales is documented for the first time, and compared with acanthodian material from the Devonian of Australia and Europe. Distinctive fin spines from Mount Crean are provisionally assigned to Culmacanthus antarctica Young, 1989b. Several features on the most complete of the new fish specimens - in particular, the apparent lack of an enlarged cheek plate - suggest a revision of the diagnosis for the Diplacanthidae.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Inhomogeneous Fractional Diffusion Equations

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05

Research on reliability evaluation of reconfigurable manufacturing system

It is a crucial task to evaluate the reliability of manufacturing process in product development process. Process reliability is a measurement of production ability of reconfigurable manufacturing system (RMS), which serves as an integrated performance indicator of the production process under specified technical constraints, including time, cost and quality. An integration framework of manufacturing process reliability evaluation is presented together with product development process. A mathematical model and algorithm based on universal generating function (UGF) is developed for calculating the reliability of manufacturing process with respect to task intensity and process capacity, which are both independent random variables. The rework strategies of RMS are analyzed under different task intensity based on process reliability is presented, and the optimization of rework strategies based on process reliability is discussed afterwards.

Randomized Push-Out Mechanisms in Priority Queuing and their Probability Characteristics

2002 Mathematics Subject Classification: 60K25.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

On the duration of negative surplus

Doutoramento em Matemática

On Some Unifications Arising from the MIMO Rician Shadowed Model

This paper shows that the proposed Rician shadowed model for multi-antenna communications allows for the unification of a wide set of models, both for multiple-input multiple-output (MIMO) and single- input single-output (SISO) communications. The MIMO Rayleigh and MIMO Rician can be deduced from the MIMO Rician shadowed, and so their SISO counterparts. Other more general SISO models, besides the Rician shadowed, are included in the model, such as the κ-μ, and its recent generalization, the κ-μ shadowed model. Moreover, the SISO η-μ and Nakagami-q models are also included in the MIMO Rician shadowed model. The literature already presents the probability density function (pdf) of the Rician shadowed Gram channel matrix in terms of the well-known gamma- Wishart distribution. We here derive its moment generating function in a tractable form. Closed- form expressions for the cumulative distribution function and the pdf of the maximum eigenvalue are also carried out.

Low codimensional intrinsic regular submanifolds in the Heisenberg group H^n

The thesis mainly concerns the study of intrinsically regular submanifolds of low codimension in the Heisenberg group H^n, called H-regular surfaces of low codimension, from the point of view of geometric measure theory. We consider an H-regular surface of H^n of codimension k, with k between 1 and n, parametrized by a uniformly intrinsically differentiable map acting between two homogeneous complementary subgroups of H^n, with target subgroup horizontal of dimension k. In particular the considered submanifold is the intrinsic graph of the parametrization. We extend various results of Ambrosio, Serra Cassano and Vittone, available for the case when k = 1. We prove that the uniform intrinsic differentiability of the parametrizing map is equivalent to the existence and continuity of its intrinsic differential, to the local existence of a suitable approximating family of Euclidean regular maps, and, when the domain and the codomain of the map are orthogonal, to the existence and continuity of suitably defined intrinsic partial derivatives of the function. Successively, we present a series of area formulas, proved in collaboration with V. Magnani. They allow to compute the (2n+2−k)-dimensional spherical Hausdorff measure and the (2n+2−k)-dimensional centered Hausdorff measure of the parametrized H-regular surface, with respect to any homogeneous distance fixed on H^n. Furthermore, we focus on (G,M)-regular sets of G, where G and M are two arbitrary Carnot groups. Suitable implicit function theorems ensure the local existence of an intrinsic parametrization of such a set, at any of its points. We prove that it is uniformly intrinsically differentiable. Finally, we prove a coarea-type inequality for a continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. We assume that the level sets of the function are uniformly lower Ahlfors regular and that the Pansu differential is everywhere surjective.

Histological features of acute tubular necrosis in native kidneys and long-term renal function

There are few studies on the relationship between the morphology of acute tubular necrosis (ATN) in native kidneys and late functional recovery. Eighteen patients with acute renal failure (ARF) who had undergone renal biopsy were studied. All had the histological diagnosis of ATN and were followed for at least six months. Clinical characteristics of ARF were analyzed, and histological features were semi-quantitatively evaluated (tubular atrophy, interstitial inflammatory infiltrate, interstitial fibrosis, and ATN). According to the maximal GFR achieved during the follow-up, patients were divided into two groups: complete recovery (GFR >= 90 mL/min/1.73 m(2)) and partial recovery (GFR < 90 mL/min/1.73 m(2)). Only 39% of the patients achieved complete recovery. Patients with partial recovery achieved their maximal GFR (63 +/- 9 mL/min/1.73 m(2)) 37 +/- 14 months after ARF, a period of time similar to those patients with complete recovery (i.e., 54 +/- 22 months). Patients with partial recovery had more severe ARF: oliguria was more frequent (90 versus 17%, p < 0.01), and they had higher peak creatinine (13.85 +/- 1.12 versus 8.95 +/- 1.30 mg/dL, p = 0.01), and longer hospitalization (45 +/- 7 versus 20 +/- 4 days, p = 0.03). No single histological parameter was associated with partial recovery, but the sum of all was when expressed as an injury index [4.00 (2.73-5.45) versus 2.00 (1.25-3.31), p < 0.05]. In conclusion, among patients with atypical ATN course, those with more severe ARF and tubule-interstitial lesions are more prone to partial recovery.