Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.Comment: 19 pages, 11 tables, 3 figures. Email address of first author has been corrected. Ref.[5] has been corrected, as has an error in Fig.3. Formatting error in Sec.4 has been corrected and the placement of tables and figures has been improved. A new paragraph has been added to Sec.4 and another new paragraph to the end of the Appendi

Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added. Minor typos have been correcte

State-independent quantum violation of noncontextuality in four dimensional space using five observables and two settings

Recently, a striking experimental demonstration [G. Kirchmair \emph{et al.}, Nature, \textbf{460}, 494(2009)] of the state-independent quantum mechanical violation of non-contextual realist models has been reported for any two-qubit state using suitable choices of \emph{nine} product observables and \emph{six} different measurement setups. In this report, a considerable simplification of such a demonstration is achieved by formulating a scheme that requires only \emph{five} product observables and \emph{two} different measurement setups. It is also pointed out that the relevant empirical data already available in the experiment by Kirchmair \emph{et al.} corroborate the violation of the NCR models in accordance with our proof

Addressing conflicts of interest in Public Private Partnerships

<p>Abstract</p> <p>Background</p> <p>Many articles have been written on conflicts of interests (COIs) in fields such as medicine, business, politics, public service and education. With the growing abundance of Public Private Partnerships (PPPs), often involving complex relationships among the partners, it is important to understand how COIs can be mitigated and managed in PPPs.</p> <p>Discussion</p> <p>We wanted to study PPPs, particularly in the areas of global health and agriculture, but discovered no single source of information available to identify and compare various approaches for avoiding and managing COIs in PPPs. This is a significant gap, especially for those wishing to study, compare and strengthen existing COI policies related to PPPs. In order to bridge this gap, we reviewed how PPPs currently address COIs and highlight what might be considered good practice in developing COI policies. We reviewed the online COI policies of 10 PPPs in global health and agriculture, and interviewed two global health PPP chief executives.</p> <p>Summary</p> <p>Based on our review of policies and interviews, we conclude that there exists a range of good practices including attention to accountability and governance, acknowledgement and disclosure, abstention and withdrawal, reporting and transparency, and independent monitoring. There appears to be a need for PPPs to interact closely and learn from each other on these parameters and to also place more emphasis on independent external monitoring of COIs as a means of strengthening their major social objectives on which their activities are largely predicated. We also recommend the establishment of a web based database, which would serve as a forum to discuss COI issues and how they can be resolved.</p

Channel choice complications:Exploring the multiplex nature of citizens' channel choices

Part 2: E-Government Services and Open GovernmentInternational audienceIn spite of massive investment and increased adoption of digital services, citizens continue to use traditional channels to interact with public organizations. The channel choice (CC) field of research tries to understand citizens’ interactions with public authorities to make the interaction more efficient and increase citizen satisfaction. However, most studies have been conducted either as surveys of hypothetical services or in experimental settings, leading to a lack of empirical data from actual use contexts. Therefore, we present the results of a sequential mixed methods study which combines observations of citizen-caseworker interaction in a call center, contextual interviews with callers, and a survey classifying topics from 10,000 telephone calls. We contribute to the CC field and practice with rich empirical data from studies of actual channel choices. Specifically, the study explores the multiplex nature of real-life CC and demonstrate how telephone calls can be part of a process, which occurs across both traditional and digital channels. Moreover, we identify problems, which cause telephone calls related to digital services, and classify these in two groups: information related problems and action related problems

Kochen-Specker Vectors

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R^n, on algorithms that single out those diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all 4-dim KS vector systems containing up to 24 vectors were generated and described, all 3-dim vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192 (117) vector system translated into MMP diagram notation with a new graphical representation, results on Tkadlec's dual diagrams added, several other new results added, journal version: to be published in J. Phys. A, 38 (2005). Web page: http://m3k.grad.hr/pavici

Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions

It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10^9 critical parity proofs of the Kochen-Specker theorem. The geometrical properties of the rays are described, an overview of the parity proofs contained in them is given, and examples of some of the proofs are exhibited.Comment: 17 pages, 13 tables, 3 figures. Several new references have been adde

Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem

Aravind and Lee-Elkin (1997) gave a proof of the Bell-Kochen-Specker theorem by showing that it is impossible to color the 60 directions from the center of a 600-cell to its vertices in a certain way. This paper refines that result by showing that the 60 directions contain many subsets of 36 and 30 directions that cannot be similarly colored, and so provide more economical demonstrations of the theorem. Further, these subsets are shown to be critical in the sense that deleting even a single direction from any of them causes the proof to fail. The critical sets of size 36 and 30 are shown to belong to orbits of 200 and 240 members, respectively, under the symmetries of the polytope. A comparison is made between these critical sets and other such sets in four dimensions, and the significance of these results is discussed.Comment: 2 new references added, caption to Table 9 correcte

Results of the c-TRAK TN trial: a clinical trial utilising ctDNA mutation tracking to detect molecular residual disease and trigger intervention in patients with moderate and high-risk early stage triple negative breast cancer.

BACKGROUND: Post-treatment detection of circulating tumour DNA (ctDNA) in early-stage triple negative breast cancer (TNBC) patients predicts high risk of relapse. c-TRAK-TN assessed the utility of prospective ctDNA surveillance in TNBC and the activity of pembrolizumab in patients with ctDNA detected (ctDNA+). PATIENTS AND METHODS: c-TRAK-TN, a multi-centre phase II trial, with integrated prospective ctDNA surveillance by digital PCR, enrolled patients with early-stage TNBC and residual disease following neoadjuvant chemotherapy, or, stage II/III with adjuvant chemotherapy. ctDNA surveillance comprised three monthly blood sampling to 12 months (18 months if samples were missed due to COVID), and ctDNA+ patients were randomised 2:1; intervention:observation. ctDNA results were blinded unless patients were allocated to intervention, when staging scans were done and those free of recurrence were offered pembrolizumab. A protocol amendment (16/09/2020) closed the observation group; all subsequent ctDNA+ patients were allocated to intervention. Co-primary endpoints were i) ctDNA detection rate ii) sustained ctDNA clearance rate on pembrolizumab (NCT03145961). RESULTS: 208 patients registered between 30/01/18 - 06/12/19, 185 had tumour sequenced, 171 (92·4%) had trackable mutations, and 161 entered ctDNA surveillance. Rate of ctDNA detection by 12 months was 27·3% (44/161,95%CI:20·6-34·9). Seven patients relapsed without prior ctDNA detection. 45 patients entered the therapeutic component (intervention n=31; observation n=14; 1 observation patient was re-allocated to intervention following protocol amendment). Of patients allocated intervention, 72% (23/32) had metastases on staging at time of ctDNA+, and 4 patients declined pembrolizumab. Of the five patients who commenced pembrolizumab, none achieved sustained ctDNA clearance. CONCLUSION: c-TRAK-TN is the first prospective study to assess whether ctDNA assays have clinical utility in guiding therapy in TNBC. Patients had a high rate of metastatic disease on ctDNA detection. Findings have implications for future trial design, emphasising the importance of commencing ctDNA testing early, with more sensitive and/or frequent ctDNA testing regimes