Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser

We propose and numerically demonstrate a novel simple method to produce optical Nyquist pulses based on pulse shaping in a passively mode-locked fiber laser with an in-cavity flat-top spectral filter. The proposed scheme takes advantage of the nonlinear in-cavity dynamics of the laser and offers the possibility to generate high-quality sinc-shaped pulses with widely tunable bandwidth directly from the laser oscillator. We also show that the use of a filter with a corrective convex profile relaxes the need for large nonlinear phase accumulation in the cavity by offsetting the concavity of the nonlinearly broadened pulse spectrum.

Morfometria dos forames mandibular, mentual e infraorbital de Lobo-guará Chrysocyon brachyurus, Illiger, 1815 aplicada a bloqueios anestésicos

CHAPTER II - The Chrysocyon brachyurus is the biggest South American canid which has a high frequency of dental injuries, both in wild and captivity. Thus, veterinary procedures are necessary to preserve the feeding capacity of hundreds of captive specimens worldwide. The aim of this study was to study the mandibular morphometry of maned wolf with emphasis on the establishment of anatomic references to the anesthetic blockage of the inferior alveolar and mental nerves. Therefore, 15 measurements in 22 hemimandibles of C. brachyurus adults were taken. For extra-oral technique of blockage of the inferior alveolar nerve at the level of the mandibular foramen, it is stated that the needle should be advanced, close to the medial surface of the mandibular ramus, by 11.4 mm perpendiculary from the palpable concavity. Alternatively, the needle can be introduced for 30.4 mm from the angular process at 20-25 degrees angle with the ventral margin. For blocking only the mentual nerve, it is recommended the introduction of needle for 10 mm, close to the lateral aspect of the mandibular body, at the level of the lower first premolar. The mandibular foramen showed similars position, size and symmetry in the maned wolfs specimens examined. The comparison of the data with those available for other carnivores reflects the necessity for determining these anatomical references specifically for each species.

Tectonic geomorphology assessment of the Ken River catchment near Panna, Madhya Pradesh, India

This thesis focuses on tectonic geomorphology and the response of the Ken River catchment to postulated tectonic forcing along a NE-striking monocline fold in the Panna region, Madhya Pradesh, India. Peninsular India is underlain by three northeast-trending paleotopographic ridges of Precambrian Indian basement, bounded by crustal-scale faults. Of particular interest is the Pokhara lineament, a crustal scale fault that defines the eastern edge of the Faizabad ridge, a paleotopographic high cored by the Archean Bundelkhand craton. The Pokhara lineament coincides with the monocline structure developed in the Proterozoic Vindhyan Supergroup rocks along the Bundelkhand cratonic margin. A peculiar, deeply incised meander-like feature, preserved along the Ken River where it flows through the monocline, may be intimately related to the tectonic regime of this system. This thesis examines 41 longitudinal stream profiles across the length of the monocline structure to identify any tectonic signals generated from recent surface uplift above the Pokhara lineament. It also investigates the evolution of the Ken River catchment in response to the generation of the monocline fold. Digital Elevation Models (DEM) from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) were used to delineate a series of tributary watersheds and extract individual stream profiles which were imported into MATLAB for analysis. Regression limits were chosen to define distinct channel segments, and knickpoints were defined at breaks between channel segments where there was a discrete change in the steepness of the channel profile. The longitudinal channel profiles exhibit the characteristics of a fluvial system in transient state. There is a significant downstream increase in normalized steepness index in the channel profiles, as well as a general increase in concavity downstream, with some channels exhibiting convex, over-steepened segments. Normalized steepness indices and uppermost knickpoint elevations are on average much higher in streams along the southwest segment of the monocline compared to streams along the northeast segment. Most channel profiles have two to three knickpoints, predominantly exhibiting slope-break morphology. These data have important implications for recent surface uplift above the Pokhara lineament. Furthermore, geomorphic features preserved along the Ken River suggest that it is an antecedent river. The incised meander-like feature appears to be the abandoned river valley of a former Ken River course that was captured during the evolution of the landscape by what is the present day Ken River.

Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Some Inverse Problems in Analysis and Geometry

Thesis (Ph.D.)--University of Washington, 2016-08

Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Classical Invariants for Principal Series and Isomorphisms of Root Data

We develop some new techniques to calculate the Schur indicator for self-dual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator and the real-quaternionic indicator. We make progress towards developing an algorithm to decide whether or not two root data are isomorphic. When the derived group has cyclic center, we solve the isomorphism problem completely. An immediate consequence is a clean and precise classification theorem for connected complex reductive groups whose derived groups have cyclic center.

An Afriat theorem for the collective model of household consumption

We provide a nonparametric 'revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a ‘collective’ version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

TECTONIC CONTROLS ON FLUVIAL LANDSCAPE DEVELOPMENT IN CENTRAL-EASTERN PORTUGAL: INSIGHTS FROM LONG PROFILE TRIBUTARY STREAM ANALYSES

This study examines the long profiles of tributaries of the Tejo (Tagus) and Zêzere rivers in central eastern Portugal (West Iberia) in order to provide new insights into the patterns, timing and controls on drainage development during the Pleistocene to Holocene incision stage. The long profiles were extracted from lower order tributary streams associated with the trunk drainage of the Tejo River and one main tributary, the Zêzere River (Fig. 1). These streams flow through a landscape strongly influenced by variations in bedrock lithology (mainly granites and metasediments), fault structures delimiting crustal blocks with distinct uplift rates, and a base-level lowering history (tectonic uplift / eustatic). The long profiles of the tributaries of the Tejo and Zêzere rivers record a series of transient and permanent knickpoints. The permanent knickpoints have direct correlation with the bedrock strength, corresponding to the outcropping of very hard quartzites or to the transition from softer (slates/metagreywaques) to harder (granite) basement. The analyzed streams/rivers record also an older transient knickpoint/knickzone separating: a) an upstream relict graded profile, with lower steepness and higher concavity, that reflects a long period of quasi-equilibrium conditions reached after the beginning of the incision stage; and b) a downstream reach displaying a rejuvenated long profile, with steeper gradient and lower concavity, particularly for the final segment, which is often convex (Fig. 2). The rejuvenated reaches testify the upstream propagation of several incision waves that are the response of each stream to continuous or increasing crustal uplift and dominant periods of base-level lowering by the trunk drainages, coeval of low sea level conditions. The long profiles and their morphological configurations enabled spatial and relative temporal patterns of incision to be quantified for each individual tributary stream. The incision values of streams flowing in uplifted blocks of the Portuguese Central Range (PCR) (ca.380-280 m) indicate differential uplift and are higher than the incision values of streams flowing on the adjacent South Portugal planation surface – the Meseta (ca. 200 m). The normalized steepness index, calculated using the method of Wobus et al. (2006), proved to be sensitive to active tectonics, as lower ksn values were found in relict graded profiles of streams located in less uplifted blocks, (e.g. Sertã stream in the PCR), or in those flowing through tectonic depressions. Fig. 1 – Geological map of the study area. 1 – fluvial terraces (Pleistocene); 2 – sedimentary cover (Paleogene and Neogene); 3 – slates and metasandstones (Devonian); 4 – slates and quartzites (Silurian); 5 – quartzites (Ordovician); 6 – slates and metagreywackes (Precambrian to Cambrian); 7 – slates, metagreywackes and limestones (Precambrian); 8 – granites and ortogneisses; 9 – diorites and gabros; 10 - fault. SFf – Sobreira Formosa fault; Sf – Sertã fault; Pf – Ponsul fault; Gf – Grade fault. The differential uplift indicated by the distribution of the ksn values and by the fluvial incision was likely accumulated on a few major faults, as the Sobreira Formosa fault (SFf), thus corroborating the tectonic activity of these faults. Due to the fact that the relict graded profiles can be correlated with other geomorphic references documented in the study area, namely the T1 terrace of the Tagus River (with an age of ca. 1 Myr), the following incision rates can be estimated: a) for the studied streams located in uplifted blocks of the PCR, 0.38 m/kyr to 0.28 m/kyr; b) for the streams flowing on the South Portugal planation surface, 0.20 m/kyr. The differential uplift inferred between crustal blocks in the study area corroborates the neotectonic activity of the bordering faults, which has been proposed in previous studies based upon less robust data. Fig. 2 – Longitudinal profile of the Nisa stream a tributary of the Tejo River. Note the equilibrium relict profile upstream the older transient knickpoint (hatched line) and the downstream rejuvenated profile (continuous line). Legend: tKP – transient knickpoint; rKp – resistant knickpoint; Mt – schist and phyllite; Gr – granite; Hf – hornfels; Og – orthogneisse. In the inset Distance – Slope plots, fill circles correspond to the relict graded profile, crosses correspond to the rejuvenated profile located downstream the older transient knickpoint (tKP).

Tectonic and lithological controls on fluvial landscape development in central-eastern Portugal: Insights from long profile tributary stream analyses

This study examines the long profiles of tributaries of the Tagus and Zêzere rivers in Portugal (West Iberia) in order to provide new insights into patterns, timing, and controls on drainage development during the Quaternary incision stage. The studied streams are incised into a relict culminant fluvial surface, abandoned at the beginning of the incision stage. The streams flow through a landscape with bedrock variations in lithology (mainly granites and metasediments) and faulted blocks with distinct uplift rates. The long profiles of the analyzed streams record an older transitory knickpoint/knickzone separating (1) an upstream relict graded profile, with lower steepness and higher concavity, that reflects a long period of quasi-equilibrium conditions reached after the beginning of the incision stage, and (2) a downstream rejuvenated long profile, with steeper gradient and lower concavity, particularly for the final reach, which is often convex. The rejuvenated reaches testify to the upstream propagation of several incision waves, interpreted as the response of each stream to increasing crustal uplift and prolonged periods of base-level lowering by the trunk drainages, coeval with low sea level conditions. The morphological configurations of the long profiles enabled spatial and relative temporal patterns of incisions to be quantified. The incision values of streams flowing on the Portuguese Central Range (PCR; ca. 380–150 m) are variable but generally higher than the incision values of streams flowing on the adjacent South Portugal Planation Surface (SPPS; ca. 220–110 m), corroborating differential uplift of the PCR relative to the SPPS. Owing to the fact that the relict graded profiles can be correlated with the Tagus River T1 terrace (1.1–0.9 My) present in the study area, incision rates can be estimated (1) for the streams located in the PCR, 0.38–0.15 m/ky and (2) for the streams flowing on the SPPS, 0.22–0.12 m/ky. The differential uplift inferred in the study area supports the neotectonic activity of the bordering faults, as proposed in previous studies based upon other geological evidence.

Tectonic and lithological controls on fluvial landscape development in central-eastern Portugal: Insights from long profile tributary stream analyses

This study examines the long profiles of tributaries of the Tagus and Zêzere rivers in Portugal (West Iberia) in order to provide new insights into patterns, timing, and controls on drainage development during the Quaternary incision stage. The studied streams are incised into a relict culminant fluvial surface, abandoned at the beginning of the incision stage. The streams flow through a landscape with bedrock variations in lithology (mainly granites and metasediments) and faulted blocks with distinct uplift rates. The long profiles of the analyzed streams record an older transitory knickpoint/knickzone separating (1) an upstream relict graded profile, with lower steepness and higher concavity, that reflects a long period of quasi-equilibrium conditions reached after the beginning of the incision stage, and (2) a downstream rejuvenated long profile, with steeper gradient and lower concavity, particularly for the final reach, which is often convex. The rejuvenated reaches testify to the upstream propagation of several incision waves, interpreted as the response of each stream to increasing crustal uplift and prolonged periods of base-level lowering by the trunk drainages, coeval with low sea level conditions. The morphological configurations of the long profiles enabled spatial and relative temporal patterns of incisions to be quantified. The incision values of streams flowing on the Portuguese Central Range (PCR; ca. 380–150 m) are variable but generally higher than the incision values of streams flowing on the adjacent South Portugal Planation Surface (SPPS; ca. 220–110 m), corroborating differential uplift of the PCR relative to the SPPS. Owing to the fact that the relict graded profiles can be correlated with the Tagus River T1 terrace (1.1–0.9 My) present in the study area, incision rates can be estimated (1) for the streams located in the PCR, 0.38–0.15 m/ky and (2) for the streams flowing on the SPPS, 0.22–0.12 m/ky. The differential uplift inferred in the study area supports the neotectonic activity of the bordering faults, as proposed in previous studies based upon other geological evidence.