Estimation of drift and diffusion functions from time series data: A maximum likelihood framework

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This contribution develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem this contribution solves important problems concerning the applicability and the accuracy of estimated parameters.Comment: 18 pages, 2 figure

Local late Amazonian boulder breakdown and denudation rate on Mars

Inactive fan surfaces become smoother and develop desert pavement over time by weathering and erosion. We use this mechanism to estimate late Amazonian boulder breakdown and surface denudation rates on a young (1.25 Ma) (Schon et al., 2009) fan on Mars. This is done by comparing boulder size and surface relief between lobes of different ages. The boulder breakdown rate is 3.5 m/Myr, surface smoothing (denudation) rate is approximated as 0.89 m/Myr. These rates exceed previous estimates for the Amazonian by orders of magnitude. We attribute this to locality, high initial smoothing rates after morphological activity and obliquity and eccentricity-driven variation in the availability of (metastable) liquid water, which acts as a catalyst for weathering during these periods. The results have major implications for process interpretation of Martian landforms, as they imply that typical small-scale morphology may be subdued within <1 Myr

Groundwater seepage landscapes from distant and local sources in experiments and on Mars

© 2014 Author(s). Valleys with theater-shaped heads can form due to the seepage of groundwater and as a result of knickpoint (waterfall) erosion generated by overland flow. This ambiguity in the mechanism of formation hampers the interpretation of such valleys on Mars, particularly since there is limited knowledge of material properties. Moreover, the hydrological implications of a groundwater or surface water origin are important for our understanding of the evolution of surface features on Mars, and a quantification of valley morphologies at the landscape scale may provide diagnostic insights on the formative hydrological conditions. However, flow patterns and the resulting landscapes produced by different sources of groundwater are poorly understood. We aim to improve the understanding of the formation of entire valley landscapes through seepage processes from different groundwater sources that will provide a framework of landscape metrics for the interpretation of such systems. We study groundwater seepage from a distant source of groundwater and from infiltration of local precipitation in a series of sandbox experiments and combine our results with previous experiments and observations of the Martian surface. Key results are that groundwater flow piracy acts on valleys fed by a distant groundwater source and results in a sparsely dissected landscape of many small and a few large valleys. In contrast, valleys fed by a local groundwater source, i.e., nearby infiltration, result in a densely dissected landscape. In addition, valleys fed by a distant groundwater source grow towards that source, while valleys with a local source grow in a broad range of directions and have a strong tendency to bifurcate, particularly on flatter surfaces. We consider these results with respect to two Martian cases: Louros Valles shows properties of seepage by a local source of groundwater and Nirgal Vallis shows evidence of a distant source, which we interpret as groundwater flow from Tharsis

Laboratory and telescope use of the NICMOS2 128 x 128 HgCdTe array

The second generation of Hubble Space Telescope (HST) instruments will include a near-infrared instrument. This choice has driven the development of near-infrared arrays to larger sizes and lower read noises. Rockwell International has delivered an array for use in the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) instrument; this array has been dubbed NICMOS2. NICMOS2 is a 128x128 array of HgCdTe diodes In-bonded to a switched MOSFET readout. The readout was specifically designed for astronomical use with the HST requirement of low read noise a prime goal. These arrays use detector material which is similar to that used by Rockwell in previous arrays (e.g., HgCdTe produced on a sapphire substrate), but the NICMOS2 devices differ substantially from other 128x128 arrays produced by Rockwell in having a read noise of only 30 electrons when read out using appropriate correlated sampling. NICMOS2 has now been characterized in the laboratory, and it has been used on groundbased telescopes

Near-bed and surface flow division patterns in experimental river bifurcations

Understanding channel bifurcation mechanics is of great importance for predicting and managing multichannel river processes and avulsion in distributary river deltas. To date, research on river channel bifurcations has focused on factors determining the stability and evolution of bifurcations. It has recently been shown that, theoretically, the nonlinearity of the relation between sediment transport and flow discharge causes one of the two distributaries of a (slightly) asymmetrical bifurcation to grow and the other to shrink. The positive feedback introduced by this effect results in highly asymmetrical bifurcations. However, there is a lack of detailed insight into flow dynamics within river bifurcations, the consequent effect on bed load flux through bifurcating channels, and thus the impact on bifurcation stability over time. In this paper, three key parameters (discharge ratio, width-to-depth ratio, and bed roughness) were varied in order to examine the secondary flow field and its effect on flow partitioning, particularly near-bed and surface flow, at an experimental bifurcation. Discharge ratio was controlled by varying downstream water levels. Flow fields were quantified using both particle image velocimetry and ultrasonic Doppler velocity profiling. Results show that a bifurcation induces secondary flow cells upstream of the bifurcation. In the case of unequal discharge ratio, a strong increase in the secondary flow near the bed causes a larger volume of near-bed flow to enter the dominant channel compared to surface and depth-averaged flow. However, this effect diminishes with larger width-to-depth ratio and with increased bed roughness. The flow structure and division pattern will likely have a stabilizing effect on river channel bifurcations. The magnitude of this effect in relation to previously identified destabilizing effects is addressed by proposing an adjustment to a widely used empirical bed load nodal-point partition equation. Our finding implies that river bifurcations can be stable under a wider range of conditions than previously thought. Key Points Secondary flow in symmetrical bifurcations causes strong near-bed flow curvature A disproportional amount of near-bed flow enters the dominant downstream channel Flow curvature adds a stabilizing feedback on bifurcation evolution

On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise

This article reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured times series and proper data analysis. Finally real world data sets are presented pointing out the relevance of the new approach

Black female student consumers' perception of clothing store image attributes

Thesis (MScVerbruikerswet) -- Stellenbosch University, 2003)ENGLISH ABSTRACT: South Africa has a complex and dynamic marketing milieu, with a majority of black consumers. Black consumers differ with regard to their lifestyles and buying behaviour. Black women are regarded as the true buyers of products and as the largest group of consumers in potential upcoming retail markets in South Africa. The youth market is also growing, anc as the economy improves, will emerge as a major market segment. The aim of this study was to investigate black female student consumers' perceptions of the importance of store image attributes that influence clothing store image, and to determine the relationships between these perceptions and consumers' lifestyles and store choice behaviour. Some of the relevant consumer characteristics, namely demographics, lifestyles and culture, as well as certain aspects of consumer behaviour, namely perception and decision-making, that affect perceptions of store image and buying behaviour, were investigated by means of an indepth literature review. The focus was on the South African black clothing consumer. A total of 500 female respondents were selected at Technikon Northern Gauteng to partake in this study. They were proportionally selected according to the number of second and third year full time black female students per department. Questionnaires were completed in class during set sessions and in the presence of the researcher. Questionnaires comprised three categories. Section one measured consumers' perception of the importance of clothing store image attributes and consisted of nine categories, each including a varying number of subsets. Responses to the 91 questions were processed by means of a five-point Likert-type scale. Section two included 30 lifestyle items and respondents replied on a five-point Likert-type scale. The third section of the questionnaire included questions on demographics and store choice behaviour. Eighteen questions were included in this section and in the questions on store choice behaviour, respondents were required to indicate on an eight-point scale how often they shopped at selected well-known clothing stores. The questionnaire was tested during a pilot study. Factor analysis, as well as Cronbach's alpha were used to assess validity of the questionnaire and to determine its internal consistency. Mean scores and standard deviations were computed for all the valid store image attributes and lifestyle characteristics, followed by mean percentage rating of each item. Store choice behaviour was measured through frequency distribution. Pearson's correlation was performed between the differentiating variables, namely store image attributes, lifestyles, and store choice behaviour. For cluster analysis, Wards method (Squared Euclidian method and icicle piot), the multivariate analysis of variance (MANOVA) and univariate analysis (ANOVA) tests were used to determine differences between clusters. The study population reflected young female consumers in the age group 20 to 23 years with relatively high educational qualifications. They were predominantly single, mostly with one child, and preferred to live in Technikon residences. Most of them relied on public transport, specifically taxis. The time taken to reach a clothing store of their choice was indicated as approximately 30 to 45 minutes of walking. Only a few were near the clothing stores of their choice. The majority of these consumers spent less than R300 per month on clothing, and they displayed a pattern of infrequent clothing purchases. The sample profile reflected a wide selection of ethnic groups within the geographical region of Gauteng. Six of the nine store image attributes investigated were perceived as important, namely Physical facilities, Promotion, Credit facilities, Salespeople service, Merchandise requests and Store layout. Location and convenience, Various store services and Preference for salespeople was considered of less importance. From the seven lifestyle factors identified, Media usage was the most important, followed by Clothing lifestyle, Social and family involvement, Activities and interests and Community involvement. Sport activities and Up-market shopping was considered unimportant. Three distinct clusters of black female consumers were identified, based on the respondents' perceptions of the importance of store image attributes and lifestyles. Black female clothing consumers were segmented as Practical intensive, Active convenience and Informed shoppers. These three clusters differed statistically significantly, regarding the following store image attribute groups: Promotion, Physical facilities, Credit facilities, and Merchandise requests. Those attribute groups that did not significantly explain differences between the clusters were Salespeople's service, Location and convenience, Various store services, Preference for salespeople, and Credit facilifies. Among lifestyle characteristics, the following obtained the highest mean scores: Media, Clothing lifestyle, and Social and family involvement. The relationships found between store image attributes and lifestyles, as well as those attributes that are responsible for differences between clusters of shoppers could provide retailers with valuable means to identify market segments and to satisfy their specific needs. South African black consumers should not be considered as a homogenous group of consumers. Further research should be done across various cultural and ethnic groups, as well as across different gender and age groups. The South African market is highly competitive, with a wide range of stores and brands; therefore, retailers need to create a store image that appeal to a particular segment of the population to exert a major impact on clothing shopping behaviour. This study focused only on the important store image attributes, but has not investigated relationships among store image and store choice. As, a result, further research is needed to assess the impact of store choice on store image in clothing retailing.AFRIKAANSE OPSOMMING: Suid-Afrika het 'n komplekse en dinamiese bemarkingsmilieu, met 'n meerderheid swart verbruikers. Swart verbruikers verskil ten opsigte van hulle lewenstyl en koopgedrag. Swart vrouens word beskou as die werklike kopers van produkte, en as die grootste groep verbruikers in potensiële opkomende kleinhandelmarkte in Suid-Afrika. Die jeugmark is ook besig om te groei, en soos die ekonomie verbeter, sal die mettertyd ontwikkel tot 'n hoofsegment van die mark. Die doel van dié studie was om 'n ondersoek te doen na swart vroulike studente verbruikers se persepsies oor die belangrikheid van winkelbeeld eienskappe wat betrekking het op die beeld van klerewinkels, en om te bepaal hoe dié persepsies verband hou met verbruikers se lewenstyle en winkelvoorkeurgedrag. Etlike toepaslike verbruikerskenmerke, by name demografie, leefstyl en kultuur, sowel as spesifieke aspekte van verbruikersgedrag, naamlik persepsie en besluitneming, wat beskouings oor winkelbeeld en koopgedrag beïnvloed, is ondersoek deur middel van 'n in-diepte oorsig van beskikbare literatuur. Die fokus was op die Suid-Afrikaanse swart klereverbruiker. 'n Totaal van 500 vroulike respondente aan die Technikon Noord-Gauteng is geselekteer om aan hierdie studie deel te neem. Hulle is proporsioneel gekies ooreenkomstig die getal tweedeen derdejaarstudente per departement. Vraelyste is in die klaskamers ingevul tydens vasgestelde periodes en in die teenwoordigheid van die navorser. Vraelyste het bestaan uit drie gedeeltes. Deel een het die verbruiker se beskouing gemeet oor die belangrikheid van klerewinkelbeeld eienskappe, wat nege kategorieë behels, wat elk weer uit 'n verskillende getal items bestaan. Response op die 91 vrae is ingewin deur middel van 'n vyfpunt Likert-tipe skaal. Deel twee sluit 30 lewenstyl-items in, en respondente moes antwoord op 'n vyfpunt Likert-tipe skaal. Die derde deel van die vraelys sluit vrae in oor demografie en winkelvoorkeurgedrag. Agtien vrae is ingesluit in dié deel, en in die vrae oor winkelvoorkeurgedrag, is daar van respondente verwag om op 'n agtpuntskaal aan te dui hoe gereeld hulle by uitgesoekte bekende klerewinkels koop. Die vraelys is getoets tydens 'n loodsstudie, Faktoranalise, en alfakoëffisient is gebruik om geldigheid en interne konsekwentheid te ondersoek. Gemiddelde tellings en standaardafwykings is bereken vir al die geldige winkelbeeld eienskappe en leefstyl kenmerke, en daarna is die gemiddelde persentasie en 'n waarde aan elke item toegeken. Winkelvoorkeurgedrag is gemeet deur middel van frekwensieverspreiding. Pearson se korrelasie is bereken tussen die onderskeie veranderlikes, naamlik winkelbeeld eienskappe, lewenstyl, en winkelvoorkeurgedrag. Vir die ontleding van bondels is Ward se Euklidiese vierkantmetode en kegelberaming gebruik; die multivariant-ontleding van variansie (MANOVA) en eenvariant-ontledingtoetse (ANOVA-toetse) is gebruik om verskille tussen bondels te bepaal. Die steekproef is geneem uit jong vroulike verbruikers in die ouderdomsgroep 20 tot 23 jaar met relatief hoë opvoedkundige kwalifikasies. Hulle was meestalongetroud, gewoonlik met een kind, en het verkies om in Technikon-koshuise te woon. Die meeste van hulle het staatgemaak op openbare vervoer, en spesifiek op taxi's. Hulle het aangedui dat dit hulle ongeveer 30 tot 45 minute se staptyd gekos het om uit te kom by 'n klerewinkel van hulle keuse. Slegs 'n paar het naby die klerewinkels van hulle keuse gewoon. Die meeste van dié verbruikers het minder as R300 per maand op klere uitgegee, en hulle vertoon 'n patroon van ongereelde klere-aankope. Die steekproef verteenwoordig 'n wye verskeidenheid etniese groeperinge in die geografiese gebied van Gauteng. Ses van die nege ondersoekte winkelbeeld eienskappe, word as belangrik beskou, naamlik Fisiese fasiliteite, Promosie, Krediet fasiliteite, Diens deur verkoopspersoneel, Handelswareversoeke en Winkeluitleg. Plasing en gerief, Verskeie winkeldienste en Voorkeur vir verkoopspersoneel word as minder belangrik beskou. Die belangrikste lewenstyl faktore geidentifiseer, sluit in Media-gebruik, gevolg deur Kledingleefstyl, Sosiale en gesinsbetrokkenheid, Aktiwiteite en belangstellings en Gemeenskapsbetrokkenheid. Sport aktiwiteite en Top-mark aankope was onbelangrik. Drie groepe swart vroulike verbruikers is geïdentifiseer, gebaseer op die respondente se persepsie van die belangrikheid van winkelbeeld eienskappe en hul lewenstyle. Swart vroulike klerasieverbruikers is ingedeel in die klasse Prakties-intensiewe, Aktief-gerieflikheids-, en Ingeligte kopers. Hierdie drie bondels het statisties drasties verskil ten opsigte van die volgende groepe winkelbeeld eienskappe: Promosies, Fisiese fasiliteite, Kredietfasiliteite, en Handelsware-versoeke. Dié groepe kenmerke wat die verskille tussen groepe nie betekenisvol verduidelik nie, is Diens deur verkoopspersoneel, Plasing en gerief, Verskeie winkeldienste, Voorkeur vir Verkoopspersoneel, en Kredietfasiliteite. Die volgende leefstylkenmerke is in die algemeen die hoogste aangeslaan: Media, Kledingleefstyl en Sosiale en gesinsbetrokkenheid. Die verband wat daar gevind is tussen ~inkelbeeld eienskappe en lewenstyle, asook daardie kenmerke wat verskille veroorsaak tussen bondels kopers, kan aan kleinhandelaars waardevolle inligting bied om marksegmente mee te identifiseer, en om te voldoen aan die behoeftes van die onderskeie verbruikersgroepe. Suid-Afrikaanse swart verbruikers moenie beskou word as 'n homogene groep verbruikers nie. Daar behoort bykomende ondersoek gedoen te word na verskillende kulturele en etniese groepe, sowel as na 'die verskeie geslags- en ouderdomsgroepe. Die Suid-Afrikaanse mark is hoogs kompeterend, met 'n wye reeks winkels en handelsmerke; derhalwe moet kleinhandelaars 'n winkelbeeld skep wat op 'n spesifieke segment van die bevolking gerig is, ten einde 'n groot impak te kan uitoefen op klerekoopgedrag. Hierdie studie het slegs gekonsentreer op die belangrike winkelbeeld eienskappe, maar het nie die verwantskap tussen winkelbeeld en winkelkeuse ondersoek nie. Gevolglik is verdere ondersoek nodig ten einde te bepaal hoe winkelkeuse in die klerasiekleinhandel beïnvloed word deur winkelbeeld

MODEX: Laboratory experiment exploring sediment spreading of a mound under waves and currents

The dispersal of sand from submerged mounds in the nearshore is driven by the interplay of processes such as converging and recirculating flows, changing roughness, bed slope effects and wave focusing/refraction. This morphological diffusivity is key to understanding sand bars in shallow seas, tidal inlets, estuaries, and the nearshore response to human interventions such as nourishments and dredging. Most of the work on the evolution of submerged mounds has been based on fluvial studies, focusing on flow without waves. In these cases, circular mounds tend to deform to crescentic (barchan) shapes. In contrast, observations of sandbars and berms in the nearshore subjected to waves show much more complex translation and deformation behavior. This contribution introduces the laboratory MOrphological Diffusivity Experiment (MODEX) aimed at examining morphological diffusivity under different forcing conditions. The experiment particularly addresses the linkages between small scale (local) effects (e.g. bed slope, bedforms) on the adjustment of sandy mounds.Peer ReviewedPostprint (published version

Earth-like aqueous debris-flow activity on Mars at high orbital obliquity in the last million years

Liquid water is currently extremely rare on Mars, but was more abundant during periods of high obliquity in the last few millions of years. This is testified by the widespread occurrence of mid-latitude gullies: small catchment-fan systems. However, there are no direct estimates of the amount and frequency of liquid water generation during these periods. Here we determine debris-flow size, frequency and associated water volumes in Istok crater, and show that debris flows occurred at Earth-like frequencies during high-obliquity periods in the last million years on Mars. Results further imply that local accumulations of snow/ice within gullies were much more voluminous than currently predicted; melting must have yielded centimetres of liquid water in catchments; and recent aqueous activity in some mid-latitude craters was much more frequent than previously anticipated