Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

On Vague Computers

Vagueness is something everyone is familiar with. In fact, most people think that vagueness is closely related to language and exists only there. However, vagueness is a property of the physical world. Quantum computers harness superposition and entanglement to perform their computational tasks. Both superposition and entanglement are vague processes. Thus quantum computers, which process exact data without "exploiting" vagueness, are actually vague computers

Dilatonic Domain Walls

Eq.(19) is added and related issues are further clarified. Also some typos and signs a re corrected.Comment: 11p

On the Dichotomy between the Nodal and Antinodal Excitations in High-temperature Superconductors

Angle-resolved photoemission data on optimally- and under-doped high temperature superconductors reveal a dichotomy between the nodal and antinodal electronic excitations. In this paper we propose an explanation of this unusual phenomenon by employing the coupling between the quasiparticle and the commensurate/incommensurate magnetic excitations.Comment: 11 pages, 9 figure

Solving the Hierarchy Problem with a Light Singlet and Supersymmetric Mass Terms

A generalization of the Next-to-Minimal Supersymmetric Model (NMSSM) is studied in which an explicit \mu-term as well as a small supersymmetric mass term for the singlet superfield are incorporated. We study the possibility of raising the Standard Model-like Higgs mass at tree level through its mixing with a light, mostly-singlet, CP-even scalar. We are able to generate Higgs boson masses up to 145 GeV with top squarks below 1.1 TeV and without the need to fine tune parameters in the scalar potential. This model yields light singlet-like scalars and pseudoscalars passing all collider constraints.Comment: 14 pages, 4 figure

Restoring Lost Anti-HER-2 Th1 Immunity in Breast Cancer: A Crucial Role for Th1 Cytokines in Therapy and Prevention

The ErbB/B2 (HER-2/neu) oncogene family plays a critical role in the development and metastatic spread of several tumor types including breast, ovarian and gastric cancer. In breast cancer, HER-2/neu is expressed in early disease development in a large percentage of DCIS lesions and its expression is associated with an increased risk of invasion and recurrence. Targeting HER-2 with antibodies such as trastuzumab or pertuzumab has improved survival, but patients with more extensive disease may develop resistance to therapy. Interestingly, response to HER-2 targeted therapies correlates with presence of immune response genes in the breast. Th1 cell production of the cytokines interferon gamma (IFNγ) and TNFα can enhance MHC class I expression, PD-L1 expression, augment apoptosis and tumor senescence, and enhances growth inhibition of many anti-breast cancer agents, including anti-estrogens and HER-2 targeted therapies. Recently, we have identified that a loss of anti-HER-2 CD4 Th1 in peripheral blood occurs during breast tumorigenesis and is dramatically diminished, even in Stage I breast cancers. The loss of anti-HER-2 Th1 response is specific and not readily reversed by standard therapies. In fact, this loss of anti-HER-2 Th1 response in peripheral blood correlates with lack of complete response to neoadjuvant therapy and diminished disease-free survival. This defect can be restored with HER-2 vaccinations in both DCIS and IBC. Correcting the anti-HER-2 Th1 response may have significant impact in improving response to HER-2 targeted therapies. Development of immune monitoring systems for anti-HER-2 Th1 to identify patients at risk for recurrence could be critical to improving outcomes, since the anti-HER-2 Th1 response can be restored by vaccination. Correction of the cellular immune response against HER-2 may prevent recurrence in high-risk patients with DCIS and IBC at risk of developing new or recurrent breast cancer.Fil: Nocera, Nadia F.. University of Pennsylvania; Estados UnidosFil: Lee, M. Catherine. H. Lee Moffitt Cancer Center; Estados UnidosFil: De La Cruz, Lucy M.. University of Pennsylvania; Estados UnidosFil: Rosemblit, Cinthia. University of Pennsylvania; Estados UnidosFil: Czerniecki, Brian J.. H. Lee Moffitt Cancer Center; Estados Unido

Defining Oppression: An Exercise Manual for the Multicultural Educator

(From the Introduction ) This manual was created with the philosophy that multicultural education needs to examine the roots of oppression thereby establishing the connections between oppressed groups, and providing skills to enact social change. The manual covers the following areas: oppression, distribution of wealth, racism, sexism, homophobia and ableism. The exercises in this manual certainly do not represent an exhaustive study of all oppression, but do provide a basic understanding that will assist students\u27 analysis of other forms of oppression. We no longer can pretend that the melting pot ·society exists. We also can no longer allow this theory to be used to perpetuate a system of oppression. The disenfranchised can no longer afford to allow the privileged few to divide us and divert our pursuit of justice. We must continue to break through our own barriers of sexism, racism and classism so that we can truely live in a multicultural world