Thèses sur le sujet « Real rank »

The purpose of this thesis is to study the following problem. Suppose that X,Y are bounded self-adjoint operators in a Hilbert space H with their commutator [X,Y] being small. Such operators are called almost commuting. How close is the pair X,Y to a pair of commuting operators X',Y'? In terms of one operator A = X + iY, suppose that the self-commutator [A,A*] is small. How close is A to the set of normal operators? Our main result is a quantitative analogue of Huaxin Lin's theorem on almost commuting matrices. We prove that for every (n x n)-matrix A with ||A|| ≤ 1 there exists a normal matrix A' such that ||A-A'|| ≤ C||[A,A*]||¹/³. We also establish a general version of this result for arbitrary C*-algebras of real rank zero assuming that A satisfies a certain index-type condition. For operators in Hilbert spaces, we obtain two-sided estimates of the distance to the set of normal operators in terms of ||[A,A*]|| and the distance from A to the set of invertible operators. The technique is based on Davidson's results on extensions of almost normal operators, Alexandrov and Peller's results on operator and commutator Lipschitz functions, and a refined version of Filonov and Safarov's results on approximate spectral projections in C*-algebras of real rank zero. In Chapter 4 we prove an analogue of Lin's theorem for finite matrices with respect to the normalized Hilbert-Schmidt norm. It is a renement of a previously known result by Glebsky, and is rather elementary. In Chapter 5 we construct a calculus of polynomials for almost commuting elements of C*-algebras and study its spectral mapping properties. Chapters 4 and 5 are based on author's joint results with Nikolay Filonov.

This thesis studies the problem of estimating the largest possible dimension of a linear space of real matrices under the assumption that every non-zero matrix in the space has (the same) fixed rank. The complex version of this problem has been studied by R. Westwick and J. Sylvester. Sylvester introduced a technique based on the theory of Chern classes for estimating the dimension from above. The question of determining the largest dimension of a linear space of maximal-rank real n x n matrices (or, equivalently, of determining the largest number of nonsingular n x n matrices all of whose non-trivial linear combinations are non-singular) was solved by J.F. Adams, P. Lax and R. Phillips. Their proof uses Adams' solution of the vector fields on spheres problem to show that the linear spaces constructed by J. Radon and A. Hurwitz are of the largest possible dimension under this hypothesis. A number of general results on the dimensions of linear spaces of fixed-rank real matrices, as well as related questions concerning linear spaces whose non-zero matrices have rank bounded below, are due to E. Rees and K.Y. Lam. The method used to provide upper bounds for the dimension is analogous to the complex case; here Stiefel-Whitney classes and K-theory are used for the calculations. Clifford Algebras are then used to construct spaces and so provide lower bounds for the dimension. We show how calculations with Stiefel-Whitney classes together with information about the existence of certain bilinear maps enable us to determine the dimensions of spaces of real n x k matrices of fixed-rank k for all n and k with k ≤ 9. The case of fixed-rank symmetric matrices is also investigated. The main result here is that every space of real symmetric n x n matrices of fixed rank 2k + 1 must have dimension 1.

This thesis considers cloud radio access network (C-RAN), where the remote radio heads (RRHs) are equipped with renewable energy resources and can trade energy with the grid. Due to uneven distribution of mobile radio traffic and inherent intermittent nature of renewable energy resources, the RRHs may need real-time energy provisioning to meet the users demands. Given the amount of available energy resources at RRHs, the main contributions of the thesis begin with introducing realtime resource management strategies to the RRHs with a shortage of power budget to select an optimal number of user terminals based on their available energy budget. On the other hand, sparse beamforming strategies introduced in the second part of the thesis account for all RRHs with or without a shortage of power and take consideration of realistic constraints on fronthaul capacity restrictions. The proposed strategies strike an optimum balance among the total power consumption in the fronthaul through adjusting the degree of partial cooperation among RRHs, RRHs total transmit power and the maximum or total spot-market energy cost. A smart energy management strategy based on the combinatorial multi-armed bandit (CMAB) theory for C-RAN, which is powered by a hybrid of grid and renewable energy sources is studied in the last part of the thesis. A combinatorial upper confidence bound (CUCB) algorithm to maximize the overall rewards, earned as a result of minimizing the cost of energy trading at individual RRHs of the C-RAN has been introduced. Adapting to the dynamic wireless channel conditions, the proposed CUCB algorithm associates a set of optimal energy packages, to be purchased from the day-ahead markets, to a set of RRHs to minimize the total cost of energy purchase from the main power grid by dynamically forming super arms. A super arm is formed on the basis of calculating the instantaneous energy demands at the current time slot, learning from the cooperative energy trading at the previous time slots and adjusting the mean rewards of the individual arms.

Gut-associated lymphoid tissues such as Peyer’s patches (PP) are inductive sites for immune response in the intestine. Unlike other peripheral lymphoid tissues, gut-associated lymphoid tissues lack afferent lymphatics and can directly sample mucosal antigens by specialized epithelial cells in the follicular associated epithelia (FAE), known as M cells. M cells derive from Lgr5+ intestinal stem cells in intestinal crypts, where the daughter cells of Lgr5+ cells differentiate into M cells after stimulation from the cytokine receptor activator of nuclear factor-κB ligand (RANKL). RANKL is produced by stromal cells within the sub-epithelial dome (SED) residing below the FAE. The transcytosis of antigens across the FAE by M cells is an important initial step in the induction of efficient mucosal immune responses against certain pathogenic bacteria as well as the commensal bacterial flora. However some pathogens, for example orally-acquired prions, may also exploit M cells to infect the host. M cells have been implicated in the uptake of orally acquired prions from the gut lumen. After oral exposure, the accumulation of prions in PP is important for their efficient spread to the nervous system. Previous studies have also shown that pathogen-induced inflammation increases M cell density and this effect can be mimicked by exogenous administration of RANKL. This has led to the hypothesis tested in this thesis that inflammation-related enhancement of M cell differentiation aids the delivery of prions into the lamina propria of villi. The administration of RANKL resulted in increased M cell density in the gut epithelium of mice. Consequently, RANKL treatment enhanced the accumulation of orally-administered prions in PP, decreased disease incubation time and increased prion disease susceptibility. These data indicate the importance of M cells in prion disease pathogenesis and highlight the potential of M cells as vaccine targets against prion disease. The fate and terminal differentiation of distinct intestinal epithelial cell lineages from their uncommitted precursors is dependent on their intrinsic expression of one or more specific transcription factors during their development. Alongside inducing M cell differentiation, RANKL stimulation can also induce the nuclear translocation of the NF-κB transcription factor subunit c-Rel. A comparison of the genes encoding the individual NF-κB subunits c-Rel, Rel-A and Rel-B revealed that they were expressed at the mRNA level in the FAE and by M cells. A c-Rel-deficiency in mice did not influence the expression of RANKL or RANK in PP. The subsequent induction of M cell maturation in the FAE was also unaffected in, indicating that c-Rel is dispensable for the RANKL-mediated differentiation and functional maturation of M cells. The factors implicated in Lgr5+ intestinal stem cell proliferation and their differentiation into M cells are poorly understood. Some reports have indicated that crypt-associated macrophages may provide extrinsic factors that assist Lgr5+ intestinal stem cell proliferation. In this thesis, the ablation of macrophages in the gut resulted in dysregulation of crypt microarchitecture, depleting Paneth cells and the Lgr5+ stem cells. This adversely affected the subsequent differentiation of intestinal epithelial cell lineages and impeded the functional development of M cells. These data reveal a previously unknown role for macrophages in the maintenance of intestinal crypts and intestinal stem cell proliferation and differentiation.

UVOD: Komplikacije terminalne bubrežne isuficijencije (TBI) kada se jačina glomerularne filtracije (JGF) smanji ispod 10 mL/min moguće je lečiti jedino hroničnom dijalizom ili transplantacijom bubrega tj. nadoknadom potpuno ili delimično izgubljene bubrežne funkcije. Uz blagovremenu edukaciju bolesnika o progresivnom toku hronične bubrežne bolesti, mogućnostima dijaliznog tretmana i transplantacije bubrega, treba na vreme obezbediti stalni funkcionalni vaskularni pristup za hemodijalizu (HD) hirurškom intervencijom kreiranja arteriovenske fistule (AVF), po mogućnosti najmanje 6 meseci pre anticipiranog započinjanja HD, jer je za njenu maturaciju potrebno 4 do 6 nedelja. Primarna AVF je opštepreporučeni najbolji stalni vaskularni pristup za bolesnike kod kojih se planira hemodijaliza. Najčešći razlog za disfunkciju vaskularnog pristupa za hemodijalizu su u 80% slučajeva trombozne komplikacije, koje se u 90% slučajeva javljaju na venskom segmentu AVF i posledica su progresivne venske neointimalne hiperplazije. Pored histoloških karakteristika zida venskog krvnog suda i hemodinamskih uslova, u etiopatogenezi ovog »adaptivnog odgovora« vrlo značajnu ulogu igraju endotel i ostale komponente hemostaznog sistema (trombocitna, koagulaciona i fibrinolizna), imunološki i citološki činioci i genetski faktori. Prevencija nastanka rane tromboze vaskularnog pristupa za hemodijalizu kod bolesnika sa TBI je moguća primenom antitromboznih lekova, tj. antitrombocitne ili antikoagulantne terapije. CILJ: Proceniti efikasnost primenjenih antitromboznih lekova (tiklopidina i nadroparin-kalcijuma) u prevenciji nastanka rane tromboze/afunkcionalnosti AVF za hemodijalizu za vreme njene maturacije unutar 6 nedelja od kreiranja u bolesnika sa TBI. Ispitati nivo biomarkera hemostaznog sistema i markere trombofilije u bolesnika sa TBI pre kreiranja AVF u cilju dopune uzroka nastanka rane tromboze/afunkcionalnosti arteriovenskih fistula za hemodijalizu. Ispitati učestalost trombofilije i njen uticaj na funkcionalnost AVF i uporediti efikasnost primenjenih preventivnih režima između bolesnika sa i bez trombofilije. MATERIJAL I METODE: U ispitivanje su uključene osobe oba pola sa prethodno postavljenom dijagnozom TBI kod kojih nisu postojale kontraindikacije za planirno hirurško kreiranje prvog stalnog vaskularnog pristupa za hemodijalizu u vidu autologne arteriovenske fistule (AAVF). Nakon hirurškog kreiranja radiocefalične arteriovenske fisule u distalnoj trećini podlaktice nedominantne ruke (89/121), intermedijalne (4/121) ili proksimalne (28/121) AAVF u studiju je uključen 121 ispitanik, koji su u cilju procene uticaja različitih antitromboznih lekova na sprečavanje nastanka rane tromboze fistula za hemodijalizu kod bolesnika sa TBI ispitanici su podeljeni u 3 grupe: Grupa I, kontrolna; 40 ispitanika koji nakon kreiranja AVF nisu dobijali antitromboznu terapiju, Grupa II; 42 ispitanika kod kojih je dan nakon kreiranja AVF započeta primena antitrombocitnog leka iz grupe tienopiridina, Ticlodix® (ticlopidin) tbl a 250 mg, 2 x ½ tbl dnevno tokom 6 nedelja i Grupa III; 39 ispitanika kod kojih je dan nakon kreiranja AVF započeta subkutana primena antikoagulantnog leka iz grupe niskomolekularnih heparina, Fraxiparine® (nadroparin-kalcijum) 2850 anti Xa i.j. (0.3 ml) dnevno tokom 6 nedelja. Jednokratno određivanje laboratorijskih parametara pokazatelja bubrežne funkcije, metabolizma glukoze i hroničnog zapaljenja, funkcionalnosti hemostaznog sistema, trombofilnih markera i genskog polimorfizma vršeno je unutar dve nedelje pre hirurškog kreiranja AAVF. Kriterijum za utvrđivanje ishoda uticaja antitrombozne terpije predstavlja maturacija AVF koja je definisana kao uspešna ako je započeto sprovođenje efikasne hemodijalize najranije 6 nedelja nakon njenog hirurškog kreiranja po proceni nadležnog nefrologa. Dijagnoza prisustva tromboze AVF postavljena je od strane nadležnog vaskularnog hirurga/nefrologa fizikalnim pregledom tokom njene maturacije, koji je podrazumevao inspekciju, palpatorno utvrđivanje odsustva karakterističnog trila i auskultatornih karakteristika protočnosti AVF ili ultarsonografskim pregledom od strane radiologa. REZULTATI: Između ispitivanih grupa u odnosu na broj tromboziranih/ afunkcionalnih AVF tokom njene maturacije (12/40 vs. 4/42 vs. 5/39; P=0.033), ustanovljena je značajna statistička razlika kao i poređenjem broja tromboziranih/afunkcionalnih AVF tokom sazrevanja u kontrolnoj grupi u odnosu na grupu ispitanika (objedinjene Grupe II i Grupa III) koja je primala antitromboznu profilaksu (12/40 vs. 9/81; P=0.009). Daljom analizom ispitivanih grupa, utvrđena je statistički značajna razlika u broju tromboziranih/afunkcionih AV fistula između kontrolne Grupe I i Grupe II (P=0.019). Testiranjem razlike u broju tromboziranih/ afunkcionalnih AVF između ispitanika kontrolne Grupe I i Grupe III nije dobijena statistički značajna razlika, kao ni između Grupe II i Grupe III. Zastupljenost broja tromboziranih/afunkcionalnih distalnih AVF za vreme njihove maturacije (12/33 vs 2/31 vs. 3/24; P=0.008) se između ispitivanih grupa značajno statistički razlikovala kao i zastupljenost tromboziranih/afunkcionalnih distalnih AVF tokom sazrevanja u kontrolnoj grupi u odnosu na grupu ispitanika koja je primala antitromboznu profilaksu (12/34 vs. 5/55; P=0.002). Testiranjem statističke razlike u broju tromboziranih/afunkcionalnih distalnih AVF između ispitanika kontrolne Grupe I i Grupe II utvrđena je statistički značajna razlika (P=0.005), dok između Grupe I i Grupe III (P=0.051), kao ni između Grupe II i Grupe III (P=0.439) nije dobijena statistički značajna razlika. Između podgrupa ispitanika kod kojih je došlo do tromboze/afunkcionalnosti AVF 21/121 (17.35%) i podgrupe ispitanika sa funkcionalno maturiranom AVF 90/121 (82.64%), značajna statistička razlika ispitanih hemostaznih parametara je bila prisutna u vrednostima agregabilnosti trombocita uz kolagen kao induktor (59.33±33.1 vs. 75.04±29.6; P=0.033). Značajna statistička razlika je zabeležena i u zastupljenosti sledećih trombofilnih markera: deficita PC (3/21 vs. 3/100; P=0.030), APC-R (4/21 vs. 5/100; P=0.026), prisustva antifosfolipidnih ACL IgM antitela (1/21 vs. 0/100; P=0.028), heterozigotnog polimorfizma FV G1691A (3/21 vs. 3/100; P=0.03) i homozigotne mutacije gena FII G20210A (1/21 vs. 0/100; P=0.028), između podgrupa bolesnika sa tromboziranom afunkcionalnom i funkcionalnom AVF. Takođe je značajna statistička razlika između podgrupa bolesnika kod kojih je došlo tromboze/afunkcionalnosti AVF i podgrupe ispitanika sa funkcionalno maturiranom AVF bila prisutna u odnosu na postojanje ranijih tromboza (23/21 vs 19/100; P=0.000) kao i zastupljenosti izolovanih venskih tromboza (9/21 vs. 2/100; P=0.000). Prediktivni potencijal pojedinačnih parametara za maturaciju AVF ispitan je univarijantnom logističkom regresionom analizom. Prilikom ispitivanja uticaja pojedinačnih parametara na maturaciju fistule, zapazili smo da su ispitanici koji su primali antitromboznu terapiju imali 3 puta veću šansu za funkcionalno maturiranu AVF [OR 3.45 (1.3-9.03)] u odnosu na bolesnike bez terapije. Ispitanici koji su imali prethodne tromboze su imali višestruko povišen rizik [OR 6.92 (2.51-19.06)] za nastanak tromboze/afunkcionalnost AVF tokom maturacije. Prilikom ispitivanja uticaja pojedinačnih parametara na rizik od pojave tromboze/afunkcionalnosti distalne AVF, zapažamo da primena antitrombozne terapije [OR 5.4 (CI 1.7 - 17.35)] petostruko snižava rizik za nastanak tromboze/ afunkcionalnosti distalne AVF, odnosno da primena antitrombozne terapije petostruko povećava šansu za adekvatnu maturaciju distalne AVF. Ispitanici koji su imali aterosklerotske KVB [OR 0.32 (0.1-0.98)] i ranije tromboze [OR 0.14 (0.04-0.44)] su imali za 68% i 86% manju verovatnoću za adekvatnu maturaciju distalne AVF (334). Trombofilija je bila prisutna u 59/121 (48.8%) ispitanika. U odnosu na markere aktivacije koagulacione komponente hemostaznog sistema i inflamatorne pokazatelje, između podgrupa ispitanika sa ili bez trombofilije statistički značajna razlika je bila prisutna u vrednostima koncentracije FVIII (170.35±103.97 vs. 235.26±124.80; P=0.02) i odnosa trombociti/limfociti (181±64.58 vs. 148.11±66.15; P=0.026). U odnosu na lokalizaciju AVF, u podgrupi ispitanika sa trombofilijom i tromboziranom/ afunkcionalnom AVF, njih 8/11 su pripadale distalnim AVF, 3/11 proksimalnim AVF, dok je u podgrupi ispitanika bez trombofilije i tromboziranom/afunkcionalnom AVF, njih 9/10 imalo distalnu, a 1/10 proksimalnu AVF. U grupi bolesnika sa trombofilijom nije zabeleženo prisustvo statistički značajne razlike u efikasnosti primenjenih antitromboznih režima merene učestalošću tromboza/afunkcionalnosti AVF u odnosu na bolesnike sa trombofilijom koji nisu primali antitromboznu terapiju (5/19 vs. 2/18 vs. 4/22; P=0.493). U grupi ispitanika bez trombofilije utvrđeno je postojanje statistički značajne razlike u učestalosti tromboza/afunkcionalnosti AVF između grupe sa i bez primene antitromboznih lekova kako u ukupnom broju tromboziranih/afunkcionalnih AVF (7/21 vs. 2/24 vs. 1/17; P=0.030). Iako je zastupljenost tromboza/afunkcionalnosti AVF u bolesnika sa kombinovanom trombofilijom češća u odnosu na ispitanike koji su imali drugu vrstu ili uopšte nisu imali trombofiliju (6/18 vs. 15/103; P=0.052), ona nije dostigla statistički značajnu vrednost. ZAKLJUČAK: Profilaktička primena antitromboznih lekova (tiklopidina i nadroparin-kalcijuma) smanjuje učestalost pojave rane tromboze i pojavu primarne nefunkcionalnosti AVF za hemodijalizu tokom njene maturacije. Primena antitrombozne terapije petostruko snižava rizik za nastanak tromboze/ afunkcionalnosti distalne AVF tokom njene maturacije. Bolesnici koji su imali prethodne tromboze imaju višestruko povišen rizik za nastanak tromboze AVF tokom njene maturacije. Kod bolesnika koji su imali aterosklerotske KVB i ranije tromboze verovatnoća za adekvatnu maturaciju distalne AVF je niža za 68% , odnosno 86%. U našem istraživanju nije utvrđeno postojanje superiornosti antikoagulantne u odnosu na antitrombocitnu profilaksu tj. oba primenjena režima su bila podjednako efikasna. U terminalnoj bubrežnoj insuficijenciji prisutan je značajan poremećaj funkcionalnosti hemostaznog sistema koji se očituje u disfunkciji endotela i poremećenoj (sniženoj) funkcionalnosti trombocita, prisustvu prokoagulantnog stanja koje se manifestuje povišenom trombinskom aktivnošću, povišenom koncentracijom činilaca koagulacije i smanjenom fibrinoliznom aktivnošću. Češća zastupljenost ukupnih ranijih tromboza (arterijskih i venskih), češća zastupljenost izolovanih venskih tromboza i učestalije prisustvo trombofilije prezentovano deficitom PC, prisustvom rezistencije na APC, prisusustvom antifosfolipidnih antikardiolipinskih antitela IgM, heterozigotnog polimorfizma FV G1691A, homozigotne mutacije FII G201210A i niža vrednost agregabilnosti trombocita uz kolagen kao induktor su markeri koji su u našem ispitivanju signifikantno češće zastupljeni kod ispitanika sa trombozom/ afunkcijom AVF za hemodijalizu tokom njenog sazrevanja. Trombofilija je prisutna kod 48.8% bolesnika saTBI, ali našim ispitivanjem nije utvrđen njen uticaj na nastanak rane tromboze/afunkcionalnosti AVF izuzev u grupi bolesnika sa kombinovanom trombofilijom. Mali broj krvarećih komplikacija u našoj studiji ukazuje na bezbednost primenjenog preventivnog režima. Na osnovu dobijenih rezultata može se preporučiti profilaktička primena tiklopidina ili nadroparin-kalcijuma u preventivnim dozama kod bolesnika sa TBI neposredno nakon kreiranja AVF. Primenu profilakse tromboznih komplikacija kod bolesnika sa novokreiranom AVF preporučujemo posebno kod bolesnika koji su imali prethodne tromboze i/ili kliničke manifestacije aterosklerotskih kardiovaskularnih bolesti.
INTRODUCTION: Complications in end stage renal disease (ESRD) when the glomerular filtration rate (GFR) decreases below 10mL/min can only be treated by chronic dialysis or kidney transplant ie. total or partial renal replacement therapy. With prompt education of the patient regarding the progressive course of the chronic kidney disease, possibilities of dialysis treatment and kidney transplantation, the patient should timely be granted permanent functional vascular hemodialysis (HD) access through surgical intervention by creating arteriovenous fistula (AVF), preferably at least 6 months prior to the anticipated start of HD, as period for its maturation is between 4 and 6 weeks. Primary AVF is the generally best recommended permanent vascular access for patients planned for dialysis. The most common reason for dysfunction of the vascular access for hemodialysis are thrombotic complications in 80% of the cases, 90% of which appear in the venous segment of AVF as the consequence of progressive venous neointimal hyperplasia. Beside the histological characteristics of the venous blood vessel wall and hemodynamic conditions, in the etiopathogenesis of this “adaptive answer”, endothel and other components of the hemostatic system (platelet, coagulation and fibrinolysis), immunological and cytological components as well as genetic factors play a very important role. Prevention of occurrence of early thrombosis of vascular access for hemodialysis in patients with ESRD is possible by treatment with antithrombotic drugs, ie. antiplatelet or anticoagulant therapy. OBJECTIVE: Estimate the efficiency of applied antithrombotic drugs (ticlopidine and nadroparincalcium) in prevention of occurrence of early thrombosis/dysfunction of AVF for hemodialysis during its time of maturation within the 6 week period. Examine the level of biomarkers of the hemostatic system and thrombophilic markers in patients with ESRD before the creation of AVF with the goal of finding additional causes of occurrence of early thrombosis/dysfunction of arteriovenous fistula for hemodialysis. Determine the incidence of thrombophilia and its impact on the functionality of AVF and compare the efficiency of applied preventive regimen between patients with and without thrombophilia. MATERIAL AND METHODS: The study included persons of both sexes with previously established diagnosis of ESRD in which there were no contraindications for the planned surgical creation of the first permanent vascular access for hemodialysis in the form of autologous arteriovenous fistula (AAVF). After the surgical creation of the radiocephalic arteriovenous fistula in the distal third of the forearm of the non-dominant hand (89/121), intermedial (4/121) or proximal (28/121) AAVF, the total number of 121 patients were included in the study and divided into three groups in order to estimate the influence of different antithrombotic drugs in prevention of early thrombosis for hemodialysis in patients with ESRD: Group I, control; 40 subjects which did not receive antithrombotic therapy after the creation of AVF, Group II; 42 subjects which started receiving an antithrombotic drug from the tienopiridine group, Ticlodix® (ticlopidine) 2 x ½ of 250mg tbl, daily, during the period of 6 weeks, after the creation of AVF, and Group III; 39 subjects which started subcutaneously receiving a drug from the low-molecular weight herapin group, Fraxiparine® (nadroparine-calcium) 2850 anti Xa i.j. (0.3 ml) daily, during the period of 6 weeks. One-time determination of laboratory parameters and renal function, glucose metabolism and chronic inflammation, hemostatic system functionality, thrombophilic markers and gene polymorphism was performed within two weeks prior to surgical creation of AAVF. The criteria for determining the outcome of the impact of antithrombotic therapy is the maturation of AVF, which is defined as successful if the implementation of effective hemodialysis started at least 6 weeks after its creation, where the effectiveness of hemodialysis is estimated by a competent nephrologist. The diagnosis of the presence of AVF thrombosis was set by a competent vascular surgeon/nephrologist through physical examination during its maturation, which included inspection, palpatory determination of absence of the characteristic thrill and auscultatory characteristics of the flow of AVF, or by ultrasonographic examination by the radiologist. RESULTS: Between the groups in terms of number of thrombosed/dysfunctional AVF during its maturation (12/40 vs. 4/42 vs. 5/39, P = 0.033), a significant statistical difference was established, as well as by comparing the number of thrombosed/dysfunctional AVF during maturation in the control group compared to the group of respondents (unified Group II and Group III) which received antithrombotic prophylaxis (12/40 vs. 9/81, P = 0.009). Through further analysis of the examined groups, a statistically significant difference was observed in the number of thrombosed/dysfunctional AV fistula between the control Group I and Group II (P = 0.019). There was no statistically significant difference noticed in the numbers of thrombosed/dysfunctional AVF between the subjects in the control Group I and Group III, as well as between Group II and Group III. Presence of the number of thrombosed/dysfunctional distal AVF during their maturation (12/33 vs 2/31 vs. 3/24, P = 0.008) between the groups statistically significantly varied, as well as the presence of the number of thrombosed/dysfunctional distal AVF during the maturation in the control group as compared to the group of subjects who received antithrombotic prophylaxis (12/34 vs. 5/55; P=0.002). By testing statistical differences in the number of thrombosed/dysfunctional distal AVF between the subjects in the control Group I and Group II a statistically significant difference (P = 0.005) was established, while there was no statistically significant difference between Group I and Group III (P = 0.051), nor between Group II and Group III (P = 0.439). Among the subgroup of patients with thrombosis/dysfunction of AVF 21/121 (17.35%) and the subgroup of subjects with functionally maturated AVF 90/121 (82.64%), a statistically significant difference of the examined hemostasis parameters was present in the values of platelet aggregation with collagen as the inducer (59.33 ± 75.04 vs. 33.1 ± 29.6; P = 0.033). A significant statistical difference was recorded in the presence of the following thrombophilic markers: deficit of PC (3/21 vs. 3/100; P = 0.030), APC-R (4/21 vs. 5/100; P = 0.026), the presence of antiphospholipid ACL IgM antibodies ( 1/21 vs. 0/100; P = 0.028), heterozygous FV G1691A polymorphism (3/21 vs. 3/100; P = 0.03) and homozygous gene mutation FII G20210A (1/21 vs. 0/100; P = 0.028), between the subgroups of patients with thrombosed/dysfunctional and functional AVF. There also was a significant statistical difference between the groups of patients which encountered thrombosis/dysfunction of AVF and subgroups of subjects with functional maturated AVF in relation to the existence of previous thrombosis (23/21 vs. 19/100; P = 0.000) and the presence of isolated venous thrombosis (9/21 vs. 2/100; P = 0.000). Predictive potential of individual parameters for AVF maturation was tested by univariate logistic regression analysis. During the examination of the influence of individual parameters on fistula maturation, we observed that subjects who received antithrombotic therapy were 3 times more likely to develop functionally maturated AVF [OR 3.45 (1.3-9.03)] as compared to subjects who did not receive any treatment. Subjects which previously had thrombosis had a multiple times increased risk [OR 6.92 (2:51 to 19:06)] of developing thrombosis/dysfunctional AVF during its maturation. When examining the influence of individual parameters on the risk of thrombosis/dysfunction of the distal AVF, we noted that the implementation of antithrombotic therapy [OR 5.4 (CI 1.7 - 17:35)] reduced risk of thrombosis/dysfunction of the distal AVF by five times, ie. that the implementation of antithrombotic therapy increases the chance for adequate distal AVF maturation by five times. The subjects that had atherosclerotic cardiovascular diseases (CVD) [OR 0.32 (0.1-0.98)] or previous thrombosis [OR 0.14 (0.04-00.44)] had a 68% or 86% less chance for adequate distal AVF maturation (334). Thrombophilia was present in 59/121 (48.8%) patients. In relation to the markers of activation of coagulation components of the hemostatic system and inflammatory markers, among subgroups of subjects with or without thrombophilia a statistically significant difference was present in the FVIII concentration (170.35 ± 103.97 vs. 235.26 ± 124.80; P = 0.02) and the platelets/lymphocytes ratio (181 ± 64.58 vs. 148.11 ± 66.15; P = 0.026). In relation to the localization of AVF, in the subgroup of subjects with thrombophilia and thrombosed/dysfunctional AVF, 8/11 of them belonged to distal AVF, 3/11 proximal AVF, while in the subgroup of subjects without thrombophilia and thrombosed/dysfunctional AVF, had 9/10 distal and 1/10 proximal AVF. In the group of subjects with thrombophilia there was no record of the presence of statistically significant differences in the efficiency of antithrombotic regimen which was measured by the frequency of thrombosis/dysfunction of AVF as compared to subjects with thrombophilia which did not receive antithrombotic therapy (5/19 vs. 2/18 vs. 4/22, P = 0.493). In the group of subjects without thrombophilia statistically significant differences were found in the frequency of thrombosis/dysfunctions of AVF among groups with and without the use of antithrombotic drugs in the total number of thrombosed/dysfunctional AVF (7/21 vs. 2/24 vs. 1/17, P = 0.030). Although the presence of thrombosis/dysfunction of AVF in patients with combined thrombophilia was more frequent compared to those who had other types of, or did not have thrombophilia (6/18 vs. 15/103; P = 0.052), it did not reach a statistically significant value. CONCLUSION: Prophylactic use of antithrombotic drugs (ticlopidine and nadroparin-calcium) reduces the incidence of early thrombosis and the occurrence of primary AVF dysfunction for hemodialysis during its maturation. Implementation of antithrombotic therapy reduced risk of thrombosis/ dysfunction of the distal AVF during its maturation by five times. Patients who have had previous thrombosis have multiple times greater risk of AVF thrombosis during its maturation. In patients who had atherosclerotic CVD or previous thrombosis, the probability for adequate maturation of distal AVF is lower by 68% or 86%. In our study there was no evidence of superiority of anticoagulant compared to antiplatelet prophylaxis ie. both regimens were equally effective. In ESRD there is significant disarrangement of hemostatic system functionality, which is reflected in endothelial dysfunction and disturbed (reduced) platelet functionality, the presence of procoagulant condition that is manifested by elevated thrombin activity, increased levels of clotting factors and reduced fibrinolytic activity. More frequent presence of total previous thrombosis (arterial and venous), higher frequency of isolated venous thrombosis and frequent presence of thrombophilia presented by the deficit of PC, the presence of resistance to APC, presence of anticardiolipin antiphospholipid antibodies IgM, heterozygous FV G1691A polymorphism, homozygous mutation FII G201210A and lower value of collagen induced platelet aggregation are the markers in our study which are significantly more frequent in patients with thrombosis/dysfunction of AVF for hemodialysis during its maturation. Thrombophilia is present in 48.8% of patients with ESRD, however our study does not determine its impact on early thrombosis/dysfunction of AVF except in the group of patients with combined thrombophilia. A small number of bleeding complications in our study points to the safety of the applied preventive regimen. Based on the obtained results, prophylactic use of ticlopidine or nadroparin-calcium in preventive doses can be recommended for patients with ESRD immediately after AVF creation. Prophylactic treatment of thrombotic complications in patients with newly created AVF is recommended especially in patients who have had previous thrombosis and/or clinical manifestations of atherosclerotic cardiovascular diseases.

I investigate on the number t of real eigenvectors of a real symmetric tensor. In particular, given a homogeneous polynomial f of degree d in 3 variables, I prove that t is greater or equal than 2c+1, if d is odd, and t is greater or equal than max(3,2c+1), if d is even, where c is the number of ovals in the zero locus of f. About binary forms, I prove that t is greater or equal than the number of real roots of f. Moreover, the above inequalities are sharp for binary forms of any degree and for cubic and quartic ternary forms. Previously, I worked on the computation of the real ranks of real binary forms of degree four and five with assigned complex rank.

by Wong Wah Fung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.
Includes bibliographical references (leaves 53-54).
Introduction --- p.2
Chapter 1 --- Preliminaries --- p.3
Chapter 1.1 --- A Summary on C*-algebras --- p.3
Chapter 1.2 --- Hereditary C*-subalgebras --- p.5
Chapter 1.3 --- C*-Inductive Limit --- p.7
Chapter 1.4 --- Basic K-Theory of C*-algebras --- p.9
Chapter 2 --- C*-algebras of Real Rank Zero --- p.14
Chapter 2.1 --- Basic Properties of C*-algebras with Real Rank Zero --- p.14
Chapter 2.2 --- Strongly Morita Equivalence and Extensions --- p.30
Chapter 3 --- Simple C*-algebras --- p.42
Chapter 3.1 --- Basic Properties --- p.42
Chapter 3.2 --- Cuntz Algebras --- p.51
Bibliography --- p.53

Thesis (Ph. D.)--University of Alberta, 2010.
Title from pdf file main screen (viewed on June 24, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, [Department of] Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.

In this thesis we consider the problem of the classification of real ternary cubics, that is, plane cubic curves with real coefficients, with respect to an arithmetic invariant, the rank, and we give the decomposition of each real ternary cubic form. We prove a theorem that characterizes the reducible cubic which factors as a product of imaginary conic and a real line with respect to rank and this is a new result in the theory of real plane cubic curves.

Crime in South Africa is very close to getting out of control. There is a dramatic increase especially in violent crimes such as murder, hijacking, business robberies, house robberies, rapes and armed robberies where innocent people get killed daily. This has the public shivering in fear. The South African Police Service are responsible for the prevention and investigation of all crimes committed. The Detective Service has the unpleasant task of hunting down the criminals that are responsible for committing these crimes. When a crime is committed and a suspect is arrested, the detectives must use all techniques and methods available to them to connect the suspect with the crime. The positive linkage of a suspect with a crime can lead to a conviction in court and one less criminal on the streets of South Africa. One technique that can be used is pointing out of a crime scene. This research is all about the pointing out of crime scenes.
Police Practice
M. Tech. (Forensic Investigation)

Nowotwory nerki dotykają co roku prawie 300 tysięcy osób, a 120 tysięcy umiera z powodu tej choroby. Najczęściej spotykanym typem jest jasnokomórkowy rak nerki który stanowi ok. 80% wszystkich przypadków. Ze względu na brak typowych objawów w pierwszych stadiach, w chwili wykrycia choroby przerzuty stwierdza się już u jednej trzeciej pacjentów, a szanse na przeżycie dramatycznie maleją. Obecnie najczęściej stosowanym leczeniem jest wycięcie guza z fragmentem bądź całą nerką, a następnie chemio- lub radioterapia, które wiążą się z licznymi skutkami ubocznymi. Ze względu na wysoki stopień unaczynienia guzów, w stadium zaawansowanym, terapia opiera się na nowych lekach antyangiogennych blokujących receptory niektórych kinaz tyrozynowych. Niestety, taka forma terapii nie jest w pełni satysfakcjonująca ponieważ wydłuża czas przeżycia chorych jedynie o kilka miesięcy co więcej, nowotwór bardzo szybko wykształca oporność na stosowane leki. ccRCC tworzy guzy silnie unaczynione, ze względu na częste mutacje genu supresorowego von Hippel-Lindau i nadmierne wydzielanie czynników proangiogennych. Nabywanie przez komórki umiejętności do opuszczania pierwotnego ogniska, aktywnej migracji i osiedlania się w odległych narządach, warunkowana jest wieloma czynnikami m. in. stopniem unaczynienia, obecnością komórek układu immunologicznego, a także nabieraniem przez komórki epitelialne właściwości i fenotypu komórek mezenchymalnych. Istotną rolę, zarówno w procesie angiogenezy jak i przejścia epitelialno-mezenchymalnego pełni receptor c-Met, ponieważ stymuluje proliferację i hamuje apoptozę oraz reguluje szereg czynników odpowiedzialnych za przerzutowanie. Procesy zapalne odgrywają bardzo ważną rolę w procesie wzrostu i rozwoju nowotworu. Jednym z modulatorów odpowiedzi zapalnej jest białko MCPIP1, kodowane przez gen ZC3H12A. Białko to zaangażowane jest w negatywną regulację stanu zapalnego dzięki aktywności RNazy, która pozwala na degradację transkryptów cytokin prozapalnych. Rosnąca liczba publikacji naukowych sugeruje, że białko MCPIP1 może istotnie wpływać na rozwój nowotworu, poprzez pośrednią lub bezpośrednią regulację czynników zaangażowanych w procesy wzrostu, proliferacji czy śmierci komórkowej. Co więcej, wykazano że poziom MCPIP1 w tkance nowotworowej jest znacząco niższy w porównaniu z otaczającą zdrową, a także może regulować poziom czynników proangiogennych takich jak VEGF czy HIF. Celem niniejszej pracy doktorskiej było określenie roli białka MCPIP1 w procesach wzrostu, unaczynienia i progresji jasnokomórkowego raka nerki, a także jego wpływ na nabieranie przez komórki nowotworowe oporności na leki celowane sunitinib i sorafenib. W pierwszym etapie badań wykorzystano linie komórkowe Caki-1 oraz Caki-2 z obniżonym poziomem białka MCPIP1, a także ze stabilną nadekspresją dzikiej lub zmutowanej formy MCPIP1. Wykazano, że niski poziom białka MCPIP1 lub zahamowanie jego aktywności RNazy prowadzi do zwiększenia potencjału proliferacyjnego komórek nowotworowych oraz przyspieszenia wzrostu guzów in vivo. Dodatkowo, brak białka MCPIP1 wpływa na wzrost ilości funkcjonalnych naczyń krwionośnych w porównaniu z kontrolą. Nadekspresja dzikiej formy MCPIP1 spowalnia wzrost guzów i zmniejsza unaczynienie in vivo. W toku doświadczeń wykazano również, że od poziomu białka MCPIP1 w komórkach nowotworowych zależy aktywacja komórek endotelialnych. Zarówno komórki ccRCC z wyciszeniem jak i mutacją w domenie RNazowej MCPIP1 wydzielają zdecydowanie więcej czynników proangiogennych w porównaniu z komórkami kontrolnymi czy z nadekspresją dzikiej formy MCPIP1, co w konsekwencji wpływa na rozluźnianie połączeń komórkowych przez internalizację VE-kadheryny i aktywuje komórki endotelialne do migracji. Równocześnie, po obniżeniu aktywności MCPIP1, dochodzi do zwiększenia ekspresji genów CXCR4, SDF-1 czy c-Met, odpowiedzialnych za podziały komórkowe i przerzutowanie. Co istotne, nadekspresja MCPIP1 zmniejsza ilość powstających przerzutów oraz hamuje proces EMT. Analizując próbki kliniczne pacjentów w różnym stadium zaawansowania ccRCC wykazano, że razem z obniżającym się poziomem białka MCPIP1 w kolejnych stadiach choroby, rośnie poziom receptora c-Met oraz innych białek zaangażowanych w progresję nowotworową. W ostatnim etapie badań zaobserwowano, że mechanizm oporności na leki sunitinib i sorafenib może polegać na podwyższeniu aktywności receptora c-Met z jednoczesnym obniżeniem poziomu białka MCPIP1, co zwiększa agresywność komórek nowotworowych, ilość przerzutów oraz zmienia ich fenotyp. Podsumowując, białko MCPIP1 może być markerem zaawansowania choroby nowotworowej oraz pełnić kluczową rolę w rozwoju ccRCC, poprzez kontrolę procesu proliferacji, progresji oraz wydzielania czynników proangiogennych. Uzyskane wyniki wskazały także na zależną regulację białka MCPIP1 i receptora c-Met oraz ich wpływ na lekooporność komórek ccRCC. Biorąc pod uwagę wyniki przedstawione w niniejszej pracy i opublikowane przez inne zespoły badawcze, można zasugerować, że MCPIP1 może być uniwersalnym białkiem supresorowym.
Every year, kidney cancers affect nearly 300 000 people, and 120 000 die of this disease. The most common type is clear cell renal cell carcinoma (ccRCC) which comprises 80% of all cases. Due to the lack of typical symptoms in the first stages, at the time of diagnosis, metastases are found in one-third of patients, and the chances of survival are dramatically reduced. Currently, the most commonly used treatment is tumor excision with partial or total nefrectomy, followed by chemo- or radiotherapy, which are associated with numerous side effects. Due to high level of tumor vasculature, therapy of more advanced stages of ccRCC is based on new antiangiogenic drugs, which inhibit multiple tyrosine kinase receptors such as VEGFR or PDGFR. Treatment with small molecules showed in approximately 38% of patients significant tumor control. However, despite of the efficacy of therapy, ccRCC often develops drug resistance, and the majority of patients who receive such treatment exhibit progressive disease after one year. Formation of new blood vessels is a critical step during tumorigenesis and metastatic spread. ccRCC develops highly vascularized tumors due to common mutation in von Hippel-Lindau gene and overexpression of proangiogenic factors. The ccRCC ability to leave primary site, active migration and settle in distant organs, is orchestrated by many factors such as angiogenesis, presence of immune cells and acquisition of the properties of more aggressive, mesenchymal phenotype. C-Met receptor plays an important role in both angiogenesis and epithelial to mesenchymal transition. It stimulates proliferation, inhibits apoptosis and regulates a number of factors responsible for metastasis. Inflammatory processes play a significant role in ccRCC growth and development. One of the negative modulators of the inflammatory response is the MCPIP1 protein, encoded by the ZC3H12A gene. MCPIP1 acts as an endonuclease due to RNase activity, which allows degradation of mRNA coding proinflammatory cytokines. Recent reports suggests that the MCPIP1 protein may significantly affect tumor development through direct or indirect regulation of factors involved in the processes of growth, proliferation or cell death. Moreover, it has been shown that MCPIP1 affects expression of proangiogenic factors such as VEGF or HIFs, and its level in tumor is lower than in adjacent healthy tissue. The main aim of doctoral dissertation research was to determine the role of MCPIP1 protein in the processes of growth, vascularization and progression of clear cell renal cell carcinoma, as well as its effect on acquiring resistance to targeted drugs sunitinib and sorafenib. In the first stage of the study, Caki-1 and Caki-2 cell lines with downregulation of MCPIP1 protein, as well as with stable overexpression of the wild type MCPIP1 and mutation in PIN domain which completely abolishes endonuclease activity were used. The following work demonstrates that low level of MCPIP1 or inhibition of its RNase activity lead to an increase in the proliferative potential of tumor cells and tumor growth in vivo. In addition, lack of MCPIP1 protein increases the number of functional blood vessels compared to control. In contrast, overexpression of the MCPIP1 slows tumor growth and reduces vascularization in vivo. Conducted experiments showed that activation of endothelial cells depends on the level of MCPIP1 protein in cancer cells. Both, inhibition and mutation of MCPIP1 in ccRCC increased secretion of proangiogenic factors such as IL-6, IL-8 and VEGF compared to control or MCPIP1 overexpressed cells. In consequence, this leads to internalization of VE-cadherin, relaxation of cell-cell junctions and activation of endothelial cells migratory potential. Concominantly, MCPIP1 level affects the expression of CXCR4, SDF-1 and c-Met genes, which are responsible for cell division and metastasis. Importantly, MCPIP1 overexpression reduces the number of lung micrometastases and inhibits the EMT process. Further analysis of clinical samples of patients at various stages of ccRCC, has shown that MCPIP1 protein level decreases with cancer progression. Furthermore, the level of c-Met receptor and other factors involved in cancer progression increase with successive stages of the disease. In the last part of the study, it was observed that therapy with small molecules such as sunitinib and sorafenib increases the aggressiveness of cancer cells and amount of lung metastases. Moreover, elevated phosphorylation of c-Met receptor with simultaneous decrease in the level of MCPIP1 may be a potential mechanism of resistance to sunitinib and sorafenib treatment. In summary, the MCPIP1 protein can be one of the factors modulating tumor development and marker of ccRCC progression. MCPIP1 controls cell proliferation, migration and secretion of proangiogenic factors. Furthermore, dependent regulation of MCPIP1 protein and c-Met receptor and their effect on drug resistance has been proven during research. Considering the results presented in this dissertation and published by other researchers, it is plausible that MCPIP1 may act as universal tumor suppressor.

The objective of the project is to find a solution to reduce bike theft, in particular e-bikes. A large percentage of bikes are not locked when they are stolen, mostly due to the inconvenience of locking your bike. The goal is to improve the user-experience of a Ulock, so that locking your bike is almost effortless. After performing a user study to find out the customer requirements, ideas are generated that meet these requirements. The best idea is a Bontrager U-lock that is stored on a District+ rear rack. The U-lock blends in with the rack and has a minimum impact on the aesthetics of the e-bike. This idea is then further developed into a finished product by making use of the available prototyping facilities. The material and manufacturing method are selected, and the total production costs are calculated. The final product is verified by assembling the complete product on a physical and CAD model of the Trek District+ 7.