Using Elimination Theory to construct Rigid Matrices

The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an n x n matrix in this family are distinct primitive roots of unity of orders roughly exp(n^2 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination theory of polynomial ideals. In particular, we use results on the existence of polynomials in elimination ideals with effective degree upper bounds (effective Nullstellensatz). Using elementary algebraic geometry, we prove that the dimension of the affine variety of matrices of rigidity at most k is exactly n^2-(n-r)^2+k. Finally, we use elimination theory to examine whether the rigidity function is semi-continuous.Comment: 25 Pages, minor typos correcte

The D647N mutation of FGFR1 induces ligand-independent receptor activation

The activation loop (A-loop) of kinases, a key regulatory region, is recurrently mutated in several kinase proteins in cancer resulting in dysregulated kinase activity and response to kinase inhibitors. FGFR1 receptor tyrosine kinase represents an important oncogene and therapeutic target for solid and hematological tumors. Here we investigate the biochemical and molecular effects of D647N mutation lying in the A-loop of FGFR1.When expressed in normal and tumoral in vitro cell models, FGFR1D647N is phosphorylated also in the absence of ligands, and this is accompanied by the activation of intracellular signaling. The expression of FGFR1D647N significantly increases single and collective migration of cancer cells in vitro and in vivo, when compared to FGFR1WT. FGFR1D647N expression exacerbates the aggressiveness of cancer cells, increasing their invasiveness in vitro and augmenting their pro-angiogenic capacity in vivo.Remarkably, the D647N mutation significantly increases the sensitivity of FGFR1 to the ATP-competitive inhibitor Erdafitinib suggesting the possibility that this mutation could become a specific target for the development of new inhibitors. Although further efforts are warranted for an exhaustive description of the activation mechanisms, for the identification of more specific inhibitors and for confirming the clinical significance of mutated FGFR1D647N, overall our data demonstrate that the D647N substitution of FGFR1 is a novel pro-oncogenic activating mutation of the receptor that, when found in cancer patients, may anticipate good response to erdafitinib treatment

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Radioresistance in rhabdomyosarcomas: much more than a question of dose

Management of rhabdomyosarcoma (RMS), the most common soft tissue sarcoma in children, frequently accounting the genitourinary tract is complex and requires a multimodal therapy. In particular, as a consequence of the advancement in dose conformity technology, radiation therapy (RT) has now become the standard therapeutic option for patients with RMS. In the clinical practice, dose and timing of RT are adjusted on the basis of patients' risk stratification to reduce late toxicity and side effects on normal tissues. However, despite the substantial improvement in cure rates, local failure and recurrence frequently occur. In this review, we summarize the general principles of the treatment of RMS, focusing on RT, and the main molecular pathways and specific proteins involved into radioresistance in RMS tumors. Specifically, we focused on DNA damage/repair, reactive oxygen species, cancer stem cells, and epigenetic modifications that have been reported in the context of RMS neoplasia in both in vitro and in vivo studies. The precise elucidation of the radioresistance-related molecular mechanisms is of pivotal importance to set up new more effective and tolerable combined therapeutic approaches that can radiosensitize cancer cells to finally ameliorate the overall survival of patients with RMS, especially for the most aggressive subtypes

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of measurements for inclusion are welcomed by the author

The botanical drug PBI-05204, a supercritical CO2 extract of Nerium oleander, sensitizes alveolar and embryonal rhabdomyosarcoma to radiotherapy in vitro and in vivo

Treatment of rhabdomyosarcoma (RMS), the most common a soft tissue sarcoma in childhood, provides intensive multimodal therapy, with radiotherapy (RT) playing a critical role for local tumor control. However, since RMS efficiently activates mechanisms of resistance to therapies, despite improvements, the prognosis remains still largely unsatisfactory, mainly in RMS expressing chimeric oncoproteins PAX3/PAX7-FOXO1, and fusion-positive (FP)-RMS. Cardiac glycosides (CGs), plant-derived steroid-like compounds with a selective inhibitory activity of the Na+/K+-ATPase pump (NKA), have shown antitumor and radio-sensitizing properties. Herein, the therapeutic properties of PBI-05204, an extract from Nerium oleander containing the CG oleandrin already studied in phase I and II clinical trials for cancer patients, were investigated, in vitro and in vivo, against FN- and FP-RMS cancer models. PBI-05204 induced growth arrest in a concentration dependent manner, with FP-RMS being more sensitive than FN-RMS, by differently regulating cell cycle regulators and commonly upregulating cell cycle inhibitors p21Waf1/Cip1 and p27Cip1/Kip1. Furthermore, PBI-05204 concomitantly induced cell death on both RMS types and senescence in FN-RMS. Notably, PBI-05204 counteracted in vitro migration and invasion abilities and suppressed the formation of spheroids enriched in CD133+ cancer stem cells (CSCs). PBI-05204 sensitized both cell types to RT by improving the ability of RT to induce G2 growth arrest and counteracting the RT-induced activation of both Non‐Homologous End‐Joining and homologous recombination DSBs repair pathways. Finally, the antitumor and radio-sensitizing proprieties of PBI-05204 were confirmed in vivo. Notably, both in vitro and in vivo evidence confirmed the higher sensitivity to PBI-05204 of FP-RMS. Thus, PBI-05204 represents a valid radio-sensitizing agent for the treatment of RMS, including the intrinsically radio-resistant FP-RMS

Detection of the mosquito-borne flaviviruses, West Nile, Dengue, Saint Louis Encephalitis, Ilheus, Bussuquara, and Yellow Fever in free-ranging black howlers (Alouatta caraya) of Northeastern Argentina

Several medically important mosquito-borne flaviviruses have been detected in Argentina in recent years: Dengue (DENV), St. Louis encephalitis (SLEV), West Nile (WNV) and Yellow Fever (YFV) viruses. Evidence of Bussuquara virus (BSQV) and Ilheus virus (ILHV) activity were found, but they have not been associated with human disease. Non-human primates can act as important hosts in the natural cycle of flaviviruses and serological studies can lead to improved understanding of virus circulation dynamics and host susceptibility. From July–August 2010, we conducted serological and molecular surveys in free–ranging black howlers (Alouatta caraya) captured in northeastern Argentina. We used 90% plaque-reduction neutralization tests (PRNT90) to analyze 108 serum samples for antibodies to WNV, SLEV, YFV, DENV (serotypes 1and 3), ILHV, and BSQV. Virus genome detection was performed using generic reverse transcription (RT)-nested PCR to identify flaviviruses in 51 antibody-negative animals. Seventy animals had antibodies for one or more flaviviruses for a total antibody prevalence of 64.8% (70/108). Monotypic (13/70, 19%) and heterotypic (27/70, 39%) patterns were differentiated. Specific neutralizing antibodies against WNV, SLEV, DENV-1, DENV-3, ILHV, and BSQV were found. Unexpectedly, the highest flavivirus antibody prevalence detected was to WNV with 9 (8.33%) monotypic responses. All samples tested by (RT)-nested PCR were negative for viral genome. This is the first detection of WNV-specific antibodies in black howlers from Argentina and the first report in free-ranging non-human primates from Latin-American countries. Given that no animals had specific neutralizing antibodies to YFV, our results suggest that the study population remains susceptible to YFV. Monitoring of these agents should be strengthened to detect the establishment of sylvatic cycles of flaviviruses in America and evaluate risks to wildlife and human health.Fil: Morales, Maria Alejandra. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Fabbri, Cintia M.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Zunino, Gabriel Eduardo. Universidad Nacional de General Sarmiento. Instituto del Conurbano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kowalewski, Miguel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia". Estación Biológica de Usos Múltiples (Sede Corrientes); ArgentinaFil: Luppo, Victoria C.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Enría, Delia A.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Levis, Silvana C.. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; ArgentinaFil: Calderón, Gladys Ethel. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud "Dr. C. G. Malbran". Instituto Nacional de Enfermedades Virales Humanas; Argentin