On the Second Fundamental Theorem of Asset Pricing

Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there is no equivalent probability measure (other than $P$) under which $X^1,\ldots,X^d$ are sigma-martingales. From this we deduce the second fundamental theorem of asset pricing- that completeness of a market is equivalent to uniqueness of Equivalent Sigma-Martingale Measure (ESMM)

Integration of Planar Antennas with MMIC Active Frontends for THz Imaging Applications

In recent years, there has been constant growth in using THz frequencies or mm, sub- mm wavelengths for various applications such as: Astronomy, Atmospheric studies, security, bio-medical imaging. All these applications are now seen more feasible due to rapid enhancements of semi-conductor processing technologies. The state of the art MMIC processing techniques offering increased cut-off frequencies (> 500 GHz) of HEMT/HBT transistors open up new opportunities for integrating systems on chip along with an antenna for either Transmit/Receive architecture. The work carried out in this thesis mainly deals with the development of antenna structures which are compatible to available MMIC processes and have well defined interface with the active circuit components for microwave as well as mm/sub-mm wave applications. The thesis briefly reviews the THz applications and modern MMIC process techniques. There- after the emphasis is on various possible antenna structures which are feasible to fabricate with MMIC layer topologies. Such antenna structures are further compared in terms of their Gain, Bandwidth, Directivity, Gaussian Coupling Efficiency and Compactness. The main focus of the thesis is towards the development of multi-pixel front ends for THz imaging of concealed weapons for security applications. The requirement in this type of application is the heterodyne detection of reflected THz signals from the distant objects (> 20 m) with tightly integrated pixels constituting of antenna integrated receiver (Antenna + Mixer + LO-Multiplier chain) giving real-time video imaging. Thus the work is focused towards Co-design of Antenna + Mixer aiming towards compactness and minimizing physical area of pixel for tighter integration. One of the important results obtained in this work, is the integration of a Double Slot Antenna with a sub-harmonically pumped resistive mixer. The novelty in this work is the new geometrical placements of slots and microstrip feed network. This new topology has differential excitation of two parallel slots for broadside beam. With this new arrangement, the need of conventional power combining network from two slots is eliminated and the transistors can directly be placed between the two slots, thus minimizing the physical area. Such arrangement is fabricated and tested at frequency of 200 GHz using 50 nm HEMT process. Encouraging results are obtained with mixer conversion loss of ~15 dB with +3 dBm LO power at sub-harmonic of 100 GHz. The next key result of this thesis is the integration of a differential 2 x 2 array of microstrip patch antennas with Gilbert Cell type sub-harmonically pumped mixer. This integration is achieved using 250 nm DHBT process. Considering the antenna ohmic efficiency, mixer conversion loss and gain of IF amplifier; the overall receiver front end features a conversion gain of ~ 14±1 dB at frequency of 320 GHz when pumped with sub-harmonic LO of 160 GHz with ~4 dBm on chip power. This receiver was also tested close to 340 GHz, which is a target frequency for security imaging applications. Another important aspect of this work is to quantify the ability of a planar antenna to couple radiated power in to the THz quasi-optical system. This is often evaluated as Gaussian Coupling Efficiency or Gaussicity. Therefore MMIC integrated antennas are needed to be characterized in terms of their Gaussicity as well. For this, a new algorithm has been developed which accepts the far-field of the antenna as input and computes the optimum beam parameters (waist and its position) which maximize the Gaussicity. Furthermore this algorithm is applied to different antenna array configurations to quantify their radiation pattern for Gaussian Coupling Efficiency

140-220 GHz Imaging Front-end Based on 250 nm InP/InGaAs/InP DHBT Process

This paper presents a pre-amplified detector receiver based on a 250 nm InP/InGaAs/InP double heterojunction bipolar transistor (DHBT) process available from the Teledyne scientific. The front end consists of a double slot antenna followed by a five stage low noise amplifier and a detector, all integrated onto the same circuit. Results of measured responsivity and noise are presented. The receiver is characterized through measuring its response to hot (293) and cold (78) K terminations. Measurements of the voltage noise spectrum at the video output of the receiver are presented and can be used to derive the temperature resolution of the receiver for a specific video bandwidth

Stochastic integration based on simple, symmetric random walks

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, it gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not c\`adl\`ag in general.Comment: 16 pages, some typos correcte

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]

Frequency Dependence of Fatigue Life and Internal Heating of a Fiber-Reinforced/Ceramic-Matrix Composite

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65943/1/j.1151-2916.1994.tb04587.x.pd

Computing the kk-binomial complexity of the Thue--Morse word

Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity of an infinite word $\mathbf{x}$ maps the integer $n$ to the number of classes in the quotient, by this $k$-binomial equivalence relation, of the set of factors of length $n$ occurring in $\mathbf{x}$. This complexity measure has not been investigated very much. In this paper, we characterize the $k$-binomial complexity of the Thue--Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue--Morse word is aperiodic, its $k$-binomial complexity eventually takes only two values. In this paper, we first obtain general results about the number of occurrences of subwords appearing in iterates of the form $\Psi^\ell(w)$ for an arbitrary morphism $\Psi$. We also thoroughly describe the factors of the Thue--Morse word by introducing a relevant new equivalence relation

Capturing the systemic immune signature of a norovirus infection: an n-of-1 case study within a clinical trial.

BACKGROUND: The infection of a participant with norovirus during the adaptive study of interleukin-2 dose on regulatory T cells in type 1 diabetes (DILT1D) allowed a detailed insight into the cellular and cytokine immune responses to this prevalent gastrointestinal pathogen. METHODS: Serial blood, serum and peripheral blood mononuclear cell (PBMC) samples were collected pre-, and post-development of the infection. To differentiate between the immune response to norovirus and to control for the administration of a single dose of aldesleukin (recombinant interleukin-2, rIL-2) alone, samples from five non-infected participants administered similar doses were analysed in parallel. RESULTS: Norovirus infection was self-limited and resolved within 24 hours, with the subsequent development of anti-norovirus antibodies. Serum pro- and anti-inflammatory cytokine levels, including IL-10, peaked during the symptomatic period of infection, coincident with increased frequencies of monocytes and neutrophils. At the same time, the frequency of regulatory CD4 + T cell (Treg), effector T cell (Teff) CD4 + and CD8 + subsets were dynamically reduced, rebounding to baseline levels or above at the next sampling point 24 hours later.  NK cells and NKT cells transiently increased CD69 expression and classical monocytes expressed increased levels of CD40, HLA-DR and SIGLEC-1, biomarkers of an interferon response. We also observed activation and mobilisation of Teffs, where increased frequencies of CD69 + and Ki-67 + effector memory Teffs were followed by the emergence of memory CD8 + Teff expressing the mucosal tissue homing markers CD103 and β7 integrin. Treg responses were coincident with the innate cell, Teff and cytokine response. Key Treg molecules FOXP3, CTLA-4, and CD25 were upregulated following infection, alongside an increase in frequency of Tregs with the capacity to home to tissues. CONCLUSIONS: The results illustrate the innate, adaptive and counter-regulatory immune responses to norovirus infection. Low-dose IL-2 administration induces many of the Treg responses observed during infection