Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. To model such scenarios, we supplement the classical Fisher model of a market by introducing {\em transaction costs}. For every buyer $i$ and every good $j$, there is a transaction cost of \cij; if the price of good $j$ is $p_j$, then the cost to the buyer $i$ {\em per unit} of $j$ is p_j + \cij. This allows the same good to be sold at different (effective) prices to different buyers. We provide a combinatorial algorithm that computes $\epsilon$-approximate equilibrium prices and allocations in $O\left(\frac{1}{\epsilon}(n+\log{m})mn\log(B/\epsilon)\right)$ operations - where $m$ is the number goods, $n$ is the number of buyers and $B$ is the sum of the budgets of all the buyers

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

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

Local h∗h^*-polynomials for one-row Hermite normal form simplices

The local $h^*$-polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus in this work is on lattice simplices presented in Hermite normal form with a single non-trivial row. We prove that when the off-diagonal entries are fixed, the distribution of coefficients for the local $h^*$-polynomial of these simplices has a limit as the normalized volume goes to infinity. Further, this limiting distribution is determined by the coefficients for a relatively small normalized volume. We also provide a thorough analysis of two specific families of such simplices, to illustrate and motivate our main result

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 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

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

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

Clinically relevant radioresistant rhabdomyosarcoma cell lines: Functional, molecular and immune-related characterization

Background: The probability of local tumor control after radiotherapy (RT) remains still miserably poor in pediatric rhabdomyosarcoma (RMS). Thus, understanding the molecular mechanisms responsible of tumor relapse is essential to identify personalized RT-based strategies. Contrary to what has been done so far, a correct characterization of cellular radioresistance should be performed comparing radioresistant and radiosensitive cells with the same isogenic background. Methods: Clinically relevant radioresistant (RR) embryonal (RD) and alveolar (RH30) RMS cell lines have been developed by irradiating them with clinical-like hypo-fractionated schedule. RMS-RR cells were compared to parental isogenic counterpart (RMS-PR) and studied following the radiobiological concept of the "6Rs", which stand for repair, redistribution, repopulation, reoxygenation, intrinsic radioresistance and radio-immuno-biology. Results: RMS-RR cell lines, characterized by a more aggressive and in vitro pro-metastatic phenotype, showed a higher ability to i) detoxify from reactive oxygen species; ii) repair DNA damage by differently activating non-homologous end joining and homologous recombination pathways; iii) counteract RT-induced G2/M cell cycle arrest by re-starting growth and repopulating after irradiation; iv) express cancer stem-like profile. Bioinformatic analyses, performed to assess the role of 41 cytokines after RT exposure and their network interactions, suggested TGF-β, MIF, CCL2, CXCL5, CXCL8 and CXCL12 as master regulators of cancer immune escape in RMS tumors. Conclusions: These results suggest that RMS could sustain intrinsic and acquire radioresistance by different mechanisms and indicate potential targets for future combined radiosensitizing strategies

HDAC3 genetic and pharmacologic inhibition radiosensitizes fusion positive rhabdomyosarcoma by promoting DNA double-strand breaks

Radiotherapy (RT) plays a critical role in the management of rhabdomyosarcoma (RMS), the prevalent soft tissue sarcoma in childhood. The high risk PAX3-FOXO1 fusion-positive subtype (FP-RMS) is often resistant to RT. We have recently demonstrated that inhibition of class-I histone deacetylases (HDACs) radiosensitizes FP-RMS both in vitro and in vivo. However, HDAC inhibitors exhibited limited success on solid tumors in human clinical trials, at least in part due to the presence of off-target effects. Hence, identifying specific HDAC isoforms that can be targeted to radiosensitize FP-RMS is imperative. We, here, found that only HDAC3 silencing, among all class-I HDACs screened by siRNA, radiosensitizes FP-RMS cells by inhibiting colony formation. Thus, we dissected the effects of HDAC3 depletion using CRISPR/Cas9-dependent HDAC3 knock-out (KO) in FP-RMS cells, which resulted in Endoplasmatic Reticulum Stress activation, ERK inactivation, PARP1- and caspase-dependent apoptosis and reduced stemness when combined with irradiation compared to single treatments. HDAC3 loss-of-function increased DNA damage in irradiated cells augmenting H2AX phosphorylation and DNA double-strand breaks (DSBs) and counteracting irradiation-dependent activation of ATM and DNA-Pkcs as well as Rad51 protein induction. Moreover, HDAC3 depletion hampers FP-RMS tumor growth in vivo and maximally inhibits the growth of irradiated tumors compared to single approaches. We, then, developed a new HDAC3 inhibitor, MC4448, which showed specific cell anti-tumor effects and mirrors the radiosensitizing effects of HDAC3 depletion in vitro synergizing with ERKs inhibition. Overall, our findings dissect the pro-survival role of HDAC3 in FP-RMS and suggest HDAC3 genetic or pharmacologic inhibition as a new promising strategy to overcome radioresistance in this tumor