Abstract:
the family of human papilloma viruses (hpv) comprises more than 100 genotypes. approximately 30 of the genotypes are responsible for infections in the human anogenital area. a precisely defined algorithm with the goal of diagnosing and removing hpv for a prolonged or indefinite length of time, as well as to protect the patient from any malignant ransformation, does not currently exist. the identification of hpv strains by pcr or dna hybridization in lesional tissue provides higher security for the patients. in high-risk patients additional colposcopy, rectoscopy, and rethroscopy/cystoscopy increase the probability of proper diagnosis and the application of a reliable therapeutic strategy. removal of lesions by means of invasive methods, such as electrodessication, cryosurgery, and/or laser therapy, may be successful and could be combined pre- and postoperatively with the local application of podophyllotoxin, trichloroacetic acid, 5-fluorouracil epinephrine gel, imiquimod, cidofovir or interferon. the administration of vaccine to young patients prevents to a significant extent the clinical manifestation of the most frequent viral strains, being hpv-6,-11 and -18. the different therapeutic methods must be applied in accordance with the clinical picture, taking into account the patient's general status, the presence of concomitant diseases, as well as the local and systematic compatibility of the side effects of each remedy. the review focuses on the diagnosis and treatment options of sexually transmitted hpv-infections and includes synopsis of the most recent literature regarding new data of epidemiology, pathogenesis, ifferential diagnosis and morphology of hpv infections in humans.

Abstract:
Let K be a field, let R=K[x_1,..., x_m] be a polynomial ring with the standard Z^m-grading (multigrading), let L be a Noetherian multigraded R-module, and let F: E --> G be a finite free multigraded presentation of L over R. Given a choice S of a multihomogeneous basis of E, we construct an explicit canonical finite free multigraded resolution T(F, S) of the R-module L. In the case of monomial ideals our construction recovers the Taylor resolution. A main ingredient of our work is a new linear algebra construction of independent interest, which produces from a representation f over K of a matroid M a canonical finite complex of finite dimensional K-vector spaces T(f) that is a resolution of Ker(f). We also show that the length of T(f) and the dimensions of its components are combinatorial invariants of the matroid M, and are independent of the representation map f.

Abstract:
apoptotic pathways are providing important saveguard mechanisms in protection from cancer by eliminating altered and often harmful cells. the disturbances of cell proliferation, differentiation and apoptosis are also found on specific signal-transduction pathways within the tumour cells and between these and the immune system. the article focuses attention on the evolution of the melanocytic naevi in the direction of a dysplastic or tumour cell. the determination of single molecules as prognostic parameters within cancer genesis seems to be problematic. new hopes are being placed on the treatment with tw-37, abt-737 and tat-bim, which, to an extent, are able to support the programmed cell death. the clinical importance of these innovative therapies remains to be seen and should therefore, be viewed with considerable criticism.

Abstract:
literature data analysis, providing an exact explanation of the lichen planus pathogenesis, as well as its transition into other rare forms such as keratosis lichenoides chronica or graham lassueur piccardi little syndrome are scant, or totally missing. the chronological course of the disease, known in the literature as lichen planus, varies. some patients develop lichen planus or lichen nitidus and there is no logical explanation why. it is also not clear why single patients initially develop ulcerative lesions in the area of the mucosa and only in a few of them these lesions affect the skin. antigen mimicry and epitope spreading could be the possible pathogenic inductor in cases of lichenoid dermatoses, as well as the cause for their transition into ulcerative, exanthematous or other rare forms. the epitope spreading is probably not the leading pathogenetic factor in lichen planus but a phenomenon which occurs later. this manuscript analyzes some basic pathogenic aspects and presents some possible medical hypotheses regarding the heterogenic clinical picture and pathogenesis of lichen planus and lichenoid like pathologies of the skin which, in the near future should be analyzed in details in order to clarify several dilemmas the clinical dermatologist has to face.

Abstract:
Let $R=\Bbbk[x_1,...,x_m]$ be the polynomial ring over a field $\Bbbk$ with the standard $\mathbb Z^m$-grading (multigrading), let $L$ be a Noetherian multigraded $R$-module, let $\beta_{i,\alpha}(L)$ the $i$th (multigraded) Betti number of $L$ of multidegree $\a$. We introduce the notion of a generic (relative to $L$) multidegree, and the notion of multigraded module of generic type. When the multidegree $\a$ is generic (relative to $L$) we provide a Hochster-type formula for $\beta_{i,\alpha}(L)$ as the dimension of the reduced homology of a certain simplicial complex associated with $L$. This allows us to show that there is precisely one homological degree $i\ge 1$ in which $\beta_{i,\alpha}(L)$ is non-zero and in this homological degree the Betti number is the $\beta$-invariant of a certain minor of a matroid associated to $L$. In particular, this provides a precise combinatorial description of all multigraded Betti numbers of $L$ when it is a multigraded module of generic type.

Abstract:
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the relationship between the geometry of the spectrum and the properties of the operators in the tuple when these operators are self-adjoint. In the case when the spectrum contains an algebraic curve passing through an isolated spectral point of one of the operators we give necessary and sufficient geometric conditions for the operators in the tuple to have a common reducing subspace. We also address spectral continuity and obtain a norm estimate for the commutant of a pair of self-adjoint matrices in terms of the Hausdorff distance of their joint spectrum to a family of lines.

Abstract:
Let $Q=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ with the standard $N^n$-grading. Let $\phi$ be a morphism of finite free $N^n$-graded $Q$-modules. We translate to this setting several notions and constructions that appear originally in the context of monomial ideals. First, using a modification of the Buchsbaum-Rim complex, we construct a canonical complex $T_\bullet(\phi)$ of finite free $N^n$-graded $Q$-modules that generalizes Taylor's resolution. This complex provides a free resolution for the cokernel $M$ of $\phi$ when $\phi$ satisfies certain rank criteria. We also introduce the Scarf complex of $\phi$, and a notion of ``generic'' morphism. Our main result is that the Scarf complex of $\phi$ is a minimal free resolution of $M$ when $\phi$ is minimal and generic. Finally, we introduce the LCM-lattice for $\phi$ and establish its significance in determining the minimal resolution of $M$.

Abstract:
We introduce to the context of multigraded modules the methods of modules over categories from algebraic topology and homotopy theory. We develop the basic theory quite generally, with a view toward future applications to a wide class of graded modules over graded rings. The main application in this paper is to study the Betti poset B=B(I,k) of a monomial ideal I in the polynomial ring R=k[x_1,...,x_m] over a field k, which consists of all degrees in Z^m of the homogeneous basis elements of the free modules in the minimal free Z^m-graded resolution of I over R. We show that the order simplicial complex of B supports a free resolution of I over R. We give a formula for the Betti numbers of I in terms of Betti numbers of open intervals of B, and we show that the isomorphism class of B completely determines the structure of the minimal free resolution of I, thus generalizing with new proofs results of Gasharov, Peeva, and Welker. We also characterize the finite posets that are Betti posets of a monomial ideal.

Abstract:
a fifty-five year old caucasian male presented with infiltrated plaques and nodules on the left leg. the lesions had been present for 6 months. he presented associated cardiopathy, nephropathy and endocrinopathy. histopathological and immunohistochemical examinations confirmed the diagnosis of cutaneous diffuse b cell lymphoma. cd 20, cd 79a and ki-67 were positive. chemotherapy with cyclophosphamide, adriamycin and vincristine promoted partial remission

Abstract:
benign chronic familial pemphigus (hailey-hailey disease) is a rare autosomal dominant blistering skin disorder characterized by suprabasal cell separation (acantholysis) of the epidermis. the hailey brothers first described it in 1939. hailey-hailey disease usually appears in the third or fourth decade, although it can occur at any age. heat, sweating and friction often exacerbates the disease, and most patients have worse symptoms during summer. it is characterized clinically by a recurrent eruption of vesicles and bullae at the sites of friction and intertriginous areas. we report a 51-year-old male presenting with grey-brown hyperkeratosis with partial papillomatosis and lichenification in the axillary and inguinal areas and infiltrated erythematous lesions in the infraorbitary region, on the side of the face. biopsies obtained from inguinal and axillar areas revealed parakeratotic crusts overlying an acantholytic epidermis. a biopsy from one of the lesions from the infraorbital area showed a jessner-kanof lymphocytic infiltration. the patient was treated with antimicrobials and four days later, topical pimecrolimus was started, leading to an improvement of the clinical picture. the efficacy of pimecrolimus in our case suggests that cellular immunity couldplay a role in thepathogenesis of hailey-hailey disease.