Connections between signal processing and complex analysis

We describe one of the research lines of the Grup de Teoria de Funcions de la UAB UB, which deals with sampling and interpolation problems in signal analysis and their connections with complex function theory.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Serum glycodelin pattern during the menstrual cycle in healthy young women.

OBJECTIVE: Glycodelin (PP14) is produced by the epithelium of the endometrium and its determination in the serum is used for functional evaluation of this tissue. Given the complex regulation and the combined contraceptive and immunosuppressive roles of glycodelin, the current lack of normal values for its serum concentration in the physiological menstrual cycle, derived from a large sample number, is a problem. We have therefore established reference values from over 600 sera. DESIGN: Retrospective study using banked serum samples. SETTING: University hospital. METHODS: Measurement of blood samples daily or every second day during one full cycle. MAIN OUTCOME MEASURES: Serum concentrations of glycodelin and normal values for every such one- or two-day interval were calculated. Late luteal phase glycodelin levels were compared with ovarian hormones. Follicular phase levels were compared with stimulated cycles from patients undergoing in vitro fertilization. RESULTS: Glycodelin concentrations were low around ovulation. Highest levels were observed at the end of the luteal phase; the glycodelin serum peak was reached 6-8 days after the one for progesterone. Late luteal glycodelin levels correlated negatively with the body mass index and positively with the progesterone level earlier in the secretory (mid-luteal) phase in the same woman. No associations with other ovarian hormones were observed. Follicular phase glycodelin levels were higher in the spontaneous than in the in vitro fertilization cycles. CONCLUSIONS: Normal values taken at two- or one-day intervals demonstrate the very late appearance of high serum glycodelin levels during the physiological menstrual cycle and their correlation with progesterone occurring earlier in the cycle.

Geochemical and H-O-Sr-Nd isotope evidence for magmatic processes and meteoric-water interactions in the basal complex of La Gomera, Canary Islands

The plutonic rocks of the Basal Complex of La Gomera, Canary Islands, Spain, were studied by means of major and trace element contents and by H-O-Sr-Nd isotope compositions in order to distinguish primary magmatic characteristics and late-stage alteration products. Deciphering the effects of alteration allowed us to determine primary, plume-related compositions that indicated D- and (18)O-depletion relative to normal upper mantle, supporting the conclusions of earlier studies on the plutonic rocks of Fuerteventura and La Palma. Late-stage alteration took place during the formation of the intrusive series induced by interaction with meteoric water. Inferred isotopic compositions of the meteoric water indicate that the water infiltrated into the rock edifice at a height of about 1500 m above sea level, suggesting the existence of a subaerial volcano which was active during the intrusive activity and that it has been either distroyed or remain buried by later volcanic and landslide events.

Role of major histocompatibility complex class II expression by non-hematopoietic cells in autoimmune and inflammatory disorders: facts and fiction.

It is well established that interactions between CD4(+) T cells and major histocompatibility complex class II (MHCII) positive antigen-presenting cells (APCs) of hematopoietic origin play key roles in both the maintenance of tolerance and the initiation and development of autoimmune and inflammatory disorders. In sharp contrast, despite nearly three decades of intensive research, the functional relevance of MHCII expression by non-hematopoietic tissue-resident cells has remained obscure. The widespread assumption that MHCII expression by non-hematopoietic APCs has an impact on autoimmune and inflammatory diseases has in most instances neither been confirmed nor excluded by indisputable in vivo data. Here we review and put into perspective conflicting in vitro and in vivo results on the putative impact of MHCII expression by non-hematopoietic APCs-in both target organs and secondary lymphoid tissues-on the initiation and development of representative autoimmune and inflammatory disorders. Emphasis will be placed on the lacunar status of our knowledge in this field. We also discuss new mouse models-developed on the basis of our understanding of the molecular mechanisms that regulate MHCII expression-that constitute valuable tools for filling the severe gaps in our knowledge on the functions of non-hematopoietic APCs in inflammatory conditions.

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

Special investigation of the University of Northern Iowa Events Complex Concessions for the period October 1, 2006 through March 31, 2012

Special investigation of the University of Northern Iowa Events Complex Concessions for the period October 1, 2006 through March 31, 2012

Munc18-1 mutations that strongly impair SNARE-complex binding support normal synaptic transmission.

Synaptic transmission depends critically on the Sec1p/Munc18 protein Munc18-1, but it is unclear whether Munc18-1 primarily operates as a integral part of the fusion machinery or has a more upstream role in fusion complex assembly. Here, we show that point mutations in Munc18-1 that interfere with binding to the free Syntaxin1a N-terminus and strongly impair binding to assembled SNARE complexes all support normal docking, priming and fusion of synaptic vesicles, and normal synaptic plasticity in munc18-1 null mutant neurons. These data support a prevailing role of Munc18-1 before/during SNARE-complex assembly, while its continued association to assembled SNARE complexes is dispensable for synaptic transmission.

Induction of CTL in vivo by major histocompatibility complex class I-peptide complexes covalently associated on the cell surface.

The identification of endogenously produced antigenic peptides presented by MHC class I molecules has opened the way to peptide-based strategies for CTL induction in vivo. Here we demonstrate that the induction in vivo of CTL directed against naturally processed antigens can be triggered by injection of syngeneic cells expressing covalent major histocompatibility complex class I-peptide complexes. In the model system used, the induction of HLA-Cw3 specific cytotoxic T lymphocytes (CTL) in mice by cell surface-associated, covalent H-2Kd (Kd)-Cw3 peptide complexes was investigated. The Kd-restricted Cw3 peptide 170-179 (RYLKNGKETL), which mimics the major natural epitope recognized by Cw3-specific CTL in H-2d mice, was converted to a photoreactive derivative by replacing Arg-170 with N-beta-(4-azidosalicyloyl)-L-2,3-diaminopropionic acid. This peptide derivative was equivalent to the parental Cw3 peptide in terms of binding to Kd molecules and recognition by Cw3-specific CTL clones and could be cross-linked efficiently and selectively to Kd molecules on the surface of Con A-stimulated spleen cells from H-2d mice. Photocross-linking prevented the rapid dissociation of Kd-peptide derivative complexes that takes place under physiological conditions. Cultures of spleen cells or peritoneal exudate cells from mice inoculated i.p. with peptide-pulsed and photocross-linked cells developed a strong CTL response following antigenic stimulation in vitro. The cultured cells efficiently lysed not only target cells sensitized with the Cw3 170-179 peptide but also target cells transfected with the Cw3 gene. Moreover, their TCR preferentially expressed V beta 10 and J alpha pHDS58 segments as well as conserved junctional sequences, as has been observed previously in Cw3-specific CTL responses. In contrast, no Cw3-specific CTL response could be obtained in cultures derived from mice injected with Con A-stimulated spleen cells pulsed with the peptide derivative without photocross-linking.

Regions of mouse mammary tumor virus superantigen involved in interaction with the major histocompatibility complex class II I-A molecule.

To study the major histocompatibility complex class II I-E dependence of mouse mammary tumor virus (MMTV) superantigens, we constructed hybrids between the I-E-dependent MMTV(GR) and the I-E-independent mtv-7 superantigens and tested them in vivo. Our results suggest that, although the C-terminal third mediates I-A interaction, additional binding sites are located elsewhere in the superantigen.

Moving Beyond Teen Crash Fatality Statistics: The Go-Team Study, GOTM-000, 2013

Despite a trend of decreasing teen fatalities due to motor vehicle crashes over the past decade, they remain the leading cause of adolescent fatalities in Iowa. The purpose of this study was to create detailed case studies of each fatal motor vehicle crash involving a driver under the age of 20 that occurred in Iowa in 2009, 2010, and 2011. Data for each crash were gathered from media sources, law enforcement agencies, and the Iowa Department of Transportation. The driving records of the teens, which included their licensure history, prior traffic citations, and prior crashes, were also acquired. In addition, data about the charges filed against a teen as a result of being involved in a fatal crash were obtained. A total of 126 crashes involving 131 teen drivers that resulted in 143 fatalities were analyzed. Many findings for fatal crashes involving teen drivers in Iowa are consistent with national trends, including the overrepresentation of male drivers, crash involvement that increases with age, crash involvement per vehicle miles traveled that decreases with age, and prevalence of single-vehicle road departure crashes. Relative to national statistics, teen fatalities from crashes in Iowa are more likely to occur from midnight to 6am and from 9am to noon. Crash type varied by driver age and county population level. Teen drivers contributed to the fatal crashes at a rate of 74%; contribution of the teen driver was unknown for 11% of crashes. Speed was a factor for about 25% of the crashes for which a teen driver was at fault. The same was also true of alcohol/drug impairment. Only 20% of the rear-seat occupants of the teen drivers’ vehicles wore seat belts compared to 60% use for the front-seat occupants. Analysis of the teens’ driving records prior to the fatal crash suggests at-fault crashes and speeding violations are associated with contributing to the fatal crash.