Fractional Brownian fields, duality, and martingales

In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure and it is related to two generalizations of fractional Brownian motion known as multifractional Brownian motions. A mistake common to the existing literature regarding multifractional Brownian motions is pointed out and corrected. The Gaussian field, due to inherited ``duality'', reveals a new way of constructing martingales associated with the odd and even part of a fractional Brownian motion and therefore of the fractional Brownian motion. The existence of those martingales and their stochastic representations is the first step to the study of natural wavelet expansions associated to those processes in the spirit of our earlier work on a construction of natural wavelets associated to Gaussian-Markov processes.Comment: Published at http://dx.doi.org/10.1214/074921706000000770 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (II)

We classify all edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are pseudo-double wheels. For this, we characterize these spherical tilings by a quadratic equation for the cosine of an edge-length. By the classification, we see: there are indeed two non-congruent, edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are the same pseudo-double wheel and the cyclic list of the four inner angles of the tiles are the same. This contrasts with that every edge-to-edge spherical tiling by congruent 3-gons is determined by the skeleton and the inner angles of the skeleton. We show that for a particular spherical isohedral tiling over the pseudo-double wheel of twelve faces, the quadratic equation has a double solution and the copies of the tile also organize a spherical non-isohedral tiling over the same skeleton.Comment: 28 pages, 14 figure

Non-Aromatic Naphthalane: A Future Remedy For Oral Mucosal Lesions

Svrha je ovoga rada prikazati podatke dobivene iz nekoliko eksperimentata koje su proveli autori u vezi sa sastavom posebne frakcije Hrvatske nafte, nazvane “NeAromatskim - Visoko Steranskim (NAVS) naftalanom, te njezinim izraženim protutupalnim djelovanjem i djelovanjem na kontrolu stanične proliferacije. NAVS je dobiven iz nafte vrlo bogate steranima, koja se desetljećima uspješno upotrebljava u liječenju psorijaze (Naftalan, Ivanić Grad, Hrvatska). Proizvodi se gotovo potpunim uklanjanjem policikličkih aromata (od kojih su neki kancerogeni), čime se dobiva potpuno bezbojno ulje ugodnoga mirisa. Prigodom postupka dearomatizaije sterani su održani i čak koncentrirani, kako je i dokazano plinskom kromatografijom i vezanim sustavom plinske kromatografije i spektrometrije masa. Ti su geogeni sterani molekularnom strukturom srodni bioaktivnim spojevima, npr. kortikosteroidima i vitaminu D. Zbog tih strukturnih sličnosti, moguće je objasniti dobru učinkovitost u liječenju psorijaze NAVS-om, u čemu su rezultati obećavajući. Tijekom liječenja NAVS-om nije bilo nikakvih promjena hematoloških niti biokemijskih nalaza. In vitro studije dokazuju izraženu dozno-ovisnu inhibiciju proliferacije stanica planocelularnoga karcinoma SCC VII, ali ne i inhibiciju nemalignih fibroblasta L929, pokazujući time selektivnost u kontroli staničnoga rasta. In vivo rezultati pokazuju znatno usporavanje rasta malignoga tumora. Uzrok tome, osim u samoj kontroli proliferacije tumorskih stanica, autori također vide i u sprječavanju neoangiogeneze (poput onom vitamina D), koje još treba dokazati imunohitokemijskim studijama. Planiraju se dodatna istraživanja i razvija se animalni model oralnog planocelularnoga karcinoma u svrhu budućeg uvođenja NAVS-a u liječenje različitih bolesti oralne sluznice budući da je NAVS i učinkovit i vrlo upotrebljiv zbog superiornih organoleptičnih svojstava.The purpose of this lecture is to summarize data obtained from several experiments conducted by authors, regarding the composition of special Croatian petrol fraction reffered to as “Non Aromatic- Very rich in Steranes” (NAVS) naphthalane, as well as its potent-inflammatory and cellular growth controlling effect. NAVS is derived from ordinary brown naphthalane, particulaly rich in steranes, that has been famous for decades in the treatment of psoriasis vulgaris (Naftalan, Ivanić Grad, Croatia). NAVS was prepared by removing virtually all of its original polycyclic aromatic content (some of them are carcinogenic), which resulted in completely colourless transparent oil with a pleasant scent. Steranes were preserved and concentrated during the de-aromatisation process, as was proven by means of GC and GC-MS. These geogenic steranes have molecular skeletons analogous to bioactive compounds, such as corticosteroids and vitamin D. Due to these structure similarities, we can explain the beneficial affects in treating psoriatic patients with NAVS, which yielded promising results. NAVS treatment did not affect either haematological or biochemical findings. Further studies established In vitro dose dependant inhibition of planocellular carcinoma (SCC VII) cell proliferation, withhout interfering with nonmalignant fibroblast (L929) cells, thus showing selectivity in cell proliferation control. In vivo results showed marked delay in tumour growth. A rationale for that, besides cell proliferation control, authors see also in the antineoangiogenetic activity of NAVS (similar to vitamin D), wich is yet to bi proved through immunohistochemical studies. Future studies are planned and oral planocellular carsinoma animal models are being developed in order to introduce NAVS in the treatment of different conditions of oral mucosa, because the preparation is not only effective, but also highly applicable in oral tissues, due to its superior organoleptic properties

Obaveštajna priprema bojišta i modelovanje upotrebe snaga za operacije u urbanim sredinama

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Cold restraint-induced gastric lesions in individual- and group-stressed rats

The aim of the present study was to 1) determine the intensity of cold restraint-induced gastric lesions and core body temperature in single-and group-stressed rats, and establish a correlation between them; and 2) determine the influence of visual contact among animals during cold restraint on development of gastric stress ulcer. Therefore, adult male Wistar rats were put into individual or group restraint boxes (composed of two, three, six or nine single boxes) with or without possibility of visual contact and then exposed 2 hr to the cold (4 degrees C). Core body temperature was measured just before and after cold restraint using a digital rectal thermometar. The results showed that: 1) single stressed animals expressed significantly higher ulcer index than those stressed in group of three, six and nine rats; 2) there was no significant difference in degree of hypothermia among rats exposed to various group paradigms; and 3) there was no significant difference in ulcer index among animals stressed in conditions with or without visual contact. An absence of significant difference in ulcer index between single and paired stressed rats implies that three is the lowest number of animals per group at which an influence of group size on behavioral and adaptive mechanisms in rats exposed to cold restraint becomes manifest

Neuroprotective effect of chronic verapamil treatment on cognitive and noncognitive deficits in an experimental Alzheimer's disease in rats

It is well known that disturbance of calcium homeostasis has a significant role in the development of neurodegenerative disorders, such as Alzheimer's disease (AD). Our recent data suggest that acute treatment with the calcium antagonist verapamil can improve some behavioral deficits in an experimental model of AD. Therefore, the present study was done to establish the effect of chronically administered verapamil on cognitive and noncognitive behavior of rats with bilateral electrolytical lesions of nucleus basalis manocellularis (NBM) - an animal model of AD. The NBM lesions produce a deficit in performance of diverse behavior tests: active avoidance (AA), low level of fear (the open field test) as well as aggressive (the test of foot-shock induced aggression) and depressive (the learned helplessness test) behavior. Verapamil (1.0, 2.5, 5.0 and 10.0 mg/kg i.p.) or saline solution (1 ml/kg i.p.) were injected 24 hr after the lesion of NBM and then repeatedly administered during the next 8 days (twice a day). Performance of the two-way active avoidance test, the open field test, the foot shock-induced aggression test and the learned helplessness test were done on day 4 after the last verapamil or saline treatment (day 13 after the lesion). Verapamil in doses of 2.5 and 5.0 mg/kg significantly ameliorated the deficit in the performance of AA, the open field behavior, and the depression, but not the aggressive behavior. The obtained beneficial effect of chronic administered verapamil suggests that the regulation of calcium homeostasis during the early period after NBM lesions might be a reasonable way to prevent the behavioral deficits in an experimental model of AD

Effect of acute physostigmine and verapamil treatment on aggressive and depressive behavior in rats with lesioned nucleus basalis magnocellularis

In order to investigate the effects of physostigmine and verapamil on aggressive (test of foot shock induced aggression) and depressive (learned helplessness test) behavior, ten days after bilateral lesions of the nucleus basalis magnocellularis (NBM), adult male Wistar rats were acute treated (30 min before the test) with physostigmine (0.045, 0.060 and 0.075 mg/kg, s.c.) or verapamil (1.0, 2.5, 5.0 and 10.0 mg/kg, s.c.) Physostigmine in dose of 0.075 mg/kg and verapamil in doses 2.5 and 5.0 mg/kg significantly prolongated the escape latency period in the learned helplessness test and thus produced a consolidation of depressiveness in NBM-lesioned rats. Tn contrast to that, there was no restitution of aggressive behavior in NBM-lesioned rats treated with both drugs. It could be concluded that both physostigmine and verapamil exerts a significant influence on depressive, but not on aggressive reaction in an animal model of Alzheimer's disease

Open field behavior in nucleus basalis magnocellularis-lesioned rats treated with physostigmine and verapamil

The present study was done to investigate and compare the effect of acetylcholinesterase inhibitor, physostigmine (0.030, 0.045, 0.060 and 0.075 mg/kg sc) and Ca-antagonist, verapamil (1.0, 2.5, 5.0 and 10.0 mg/kg sc) on open field behavior in male Wistar rats with bilateral electrolytic lesions of nucleus basalis magnocellularis (NBM). NBM-lesions produced a significant increase and decrease of ambulation and number of inner squares entered, and defecation, respectively, with no influence on grooming in rats exposed to novel environment. Physostigmine and verapamil in all tested doses, given 30 min before the test did not affect the open field behavior in control animals. In contrast to that, physostigmine (0.045, 0.060 and 0.075 mg/kg) and verapamil (2.5 and 5.0 mg/kg) significantly reduced ambulation and number of inner squares entered in NBM-lesioned rats. Also, physostigmine in a dose of 0.060 mg/kg significantly decreased defecation and in doses of 0.060 and 0.075 mg/kg the grooming, as well. On the other hand, verapamil only in a dose of 2.5 mg/kg significantly increased defecation. It could be concluded that lesions of NBM in rats induced disturbances in the open field behavior, which might be successfully ameliorate by physostigmine and verapamil treatment

Modelling financial time series using reflections of copulas

summary:We have intensified studies of reflections of copulas (that we introduced recently in [6]) and found that their convex combinations exhibit potentially useful fitting properties for original copulas of the Normal, Frank, Clayton and Gumbel types. We show that these properties enable us to construct interesting models for the relations between investment in stocks and gold